G. Alessandrini, Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains, Commentarii Mathematici Helvetici, vol.69, issue.1, pp.142-154, 1994.
DOI : 10.1007/BF02564478

G. Allaire and O. Pantz, Structural optimization with $\tt{FreeFem++}$, Structural and Multidisciplinary Optimization, vol.21, issue.1, pp.173-181, 2006.
DOI : 10.1007/s00158-006-0017-y

W. K. Allard, On the First Variation of a Varifold, The Annals of Mathematics, vol.95, issue.3, pp.417-491, 1972.
DOI : 10.2307/1970868

W. K. Allard, On the First Variation of a Varifold: Boundary Behavior, The Annals of Mathematics, vol.101, issue.3, pp.418-446, 1975.
DOI : 10.2307/1970934

H. W. Alt and L. A. Caffarelli, Existence and regularity for a minimum problem with free boundary, J. Reine Angew. Math, vol.325, pp.105-144, 1981.

H. W. Alt, L. A. Caffarelli, and A. Friedman, Variational problems with two phases and their free boundaries, Transactions of the American Mathematical Society, vol.282, issue.2, pp.431-461, 1984.
DOI : 10.1090/S0002-9947-1984-0732100-6

F. Alter, V. Caselles, and A. Chambolle, Evolution of characteristic functions of convex sets in the plane by the minimizing total variation flow, Interfaces and Free Boundaries, vol.7, issue.1, pp.29-53, 2005.
DOI : 10.4171/IFB/112

C. J. Alves and P. R. Antunes, The method of fundamental solutions applied to the calculation of eigenfrequencies and eigenmodes of 2d simply connected shapes, Comp. Mat. Continua, vol.2, issue.4, pp.251-266, 2005.

H. Amann, Ordinary differential equations, volume 13 of de Gruyter Studies in Mathematics An introduction to nonlinear analysis, 1990.

L. Ambrosio and E. Paolini, Partial regularity for quasi minimizers of perimeter, Ricerche Mat, vol.48, pp.167-186, 1999.

D. E. Apushkinskaya, N. N. Ural, and ?. Tseva, On the behavior of free boundaries near the boundary of the domain, Journal of Mathematical Sciences, vol.4, issue.2, 1995.
DOI : 10.1007/BF02355579

I. Athanasopoulos and L. A. Caffarelli, Optimal Regularity of Lower-Dimensional Obstacle Problems, Journal of Mathematical Sciences, vol.42, issue.3, p.310, 2004.
DOI : 10.1007/s10958-005-0496-1

E. Barozzi, E. Gonzalez, and U. Massari, The mean curvature of a Lipschitz continuous manifold, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl, vol.14, issue.94, pp.257-277, 2003.

T. Bayen, Optimisation de formes dans la classe des corps de largeur constante et des rotors, Thèse, 2007.

G. Bellettini, V. Caselles, and M. Novaga, The Total Variation Flow in RN, Journal of Differential Equations, vol.184, issue.2, pp.475-525, 2002.
DOI : 10.1006/jdeq.2001.4150

E. Bombieri, E. De-giorgi, and E. Giusti, Minimal cones and the Bernstein problem, Inventiones mathematicae, vol.88, issue.3, pp.243-268, 1969.
DOI : 10.1007/BF01404309

T. Briançon and J. Lamboley, Regularity of the optimal shape for the first eigenvalue of the Laplacian with volume and inclusion constraints, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.26, issue.4, 2008.
DOI : 10.1016/j.anihpc.2008.07.003

T. Briançon, Problèmes de régularité en optimisation de formes, Thèse, 2002.

T. Briançon, Regularity of optimal shapes for the Dirichlet's energy with volume constraint, ESAIM: Control, Optimisation and Calculus of Variations, vol.10, issue.1, pp.99-122, 2004.
DOI : 10.1051/cocv:2003038

T. Briançon, M. Hayouni, and M. Pierre, Lipschitz continuity of state functions in some optimal shaping, Calculus of Variations and Partial Differential Equations, vol.2, issue.1, pp.13-32, 2005.
DOI : 10.1007/s00526-004-0286-5

F. Brock, V. Ferone, and B. Kawohl, A symmetry problem in the calculus of variations, Calculus of Variations and Partial Differential Equations, vol.173, issue.6, pp.593-599, 1996.
DOI : 10.1007/BF01261764

D. Bucur, Concentration-compacit?? et ??-convergence, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.327, issue.3, pp.255-258, 1998.
DOI : 10.1016/S0764-4442(98)80142-0

D. Bucur, Uniform Concentration-Compactness for Sobolev Spaces on Variable Domains, Journal of Differential Equations, vol.162, issue.2, pp.427-450, 2000.
DOI : 10.1006/jdeq.1999.3726
URL : http://doi.org/10.1006/jdeq.1999.3726

D. Bucur, Regularity of optimal convex shapes, J. Convex Anal, vol.10, issue.2, pp.501-516, 2003.

D. Bucur, Do Optimal Shapes Exist?, Milan Journal of Mathematics, vol.75, issue.1, pp.379-398, 2007.
DOI : 10.1007/s00032-007-0074-8
URL : https://hal.archives-ouvertes.fr/hal-00387014

D. Bucur, G. Buttazzo, and I. Figueiredo, On The Attainable Eigenvalues of the Laplace Operator, SIAM Journal on Mathematical Analysis, vol.30, issue.3, pp.527-536, 1999.
DOI : 10.1137/S0036141097329135

D. Bucur and A. Henrot, Minimization of the third eigenvalue of the Dirichlet Laplacian, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci, vol.456, pp.985-996, 1996.

D. Bucur and J. Zolésio, Anatomy of the shape Hessian via lie brackets, Annali di Matematica Pura ed Applicata, vol.1, issue.No. 6, pp.127-143, 1997.
DOI : 10.1007/BF01783465

G. Buttazzo and G. Dal-maso, An existence result for a class of shape optimization problems, Archive for Rational Mechanics and Analysis, vol.3, issue.2, pp.183-195, 1993.
DOI : 10.1007/BF00378167

G. Buttazzo and P. Guasoni, Shape optimization problems over classes of convex domains, J. Convex Anal, vol.4, issue.2, pp.343-351, 1997.

L. A. Caffarelli, D. Jerison, and C. E. Kenig, Global energy minimizers for free boundary problems and full regularity in three dimensions, Contemp. Math, vol.350, pp.83-97, 2004.
DOI : 10.1090/conm/350/06339

L. Capogna, C. E. Kenig, and L. Lanzani, Harmonic measure, volume 35 of University Lecture Series Geometric and analytic points of view, 2005.

G. Carlier, On a theorem of Alexandrov, J. Nonlinear Convex Anal, vol.5, issue.1, pp.49-58, 2004.

G. Carlier and T. Lachand-robert, Convex bodies of optimal shape, J. Convex Anal, vol.10, issue.1, pp.265-273, 2003.

V. Caselles, A. Chambolle, and M. Novaga, Uniqueness of the Cheeger set of a convex body, Pacific Journal of Mathematics, vol.232, issue.1, pp.77-90, 2007.
DOI : 10.2140/pjm.2007.232.77

S. Chanillo and C. E. Kenig, Regularity of the minimizers in the composite membrane problem in R 2, 2008.

J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian In Problems in analysis, pp.195-199, 1969.

J. Choe, Sharp isoperimetric inequalities for stationary varifolds and area minimizing flat chains mod k. Kodai Math, J, vol.19, issue.2, pp.177-190, 1996.

A. Cianchi and N. Fusco, Steiner symmetric extremals in P??lya???Szeg??-type inequalities, Advances in Mathematics, vol.203, issue.2, pp.673-728, 2006.
DOI : 10.1016/j.aim.2005.05.007

M. Costabel and M. Dauge, Un r??sultat de densit?? pour les ??quations de Maxwell r??gularis??es dans un domaine lipschitzien, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.327, issue.9, pp.849-854, 1998.
DOI : 10.1016/S0764-4442(99)80117-7

M. Crouzeix, Variational approach of a magnetic shaping problem, European J. Mech. B Fluids, vol.10, issue.5, pp.527-536, 1991.
URL : https://hal.archives-ouvertes.fr/inria-00075207

M. Crouzeix, Une famille d???in??galit??s pour les ensembles convexes du plan, Annales math??matiques Blaise Pascal, vol.12, issue.2, pp.223-230, 2005.
DOI : 10.5802/ambp.204

M. Crouzeix, A functional calculus based on the numerical range : applications. Linear Multilinear Algebra, pp.81-103, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00361123

M. Dambrine and M. Pierre, About stability of equilibrium shapes, ESAIM: Mathematical Modelling and Numerical Analysis, vol.34, issue.4, pp.811-834, 2000.
DOI : 10.1051/m2an:2000105

M. Dauge, Elliptic boundary value problems on corner domains, volume 1341 of Lecture Notes in Mathematics, 1988.

M. Dauge, Strongly elliptic problems near cuspidal points and edges. In Partial differential equations and functional analysis, Progr. Nonlinear Differential Equations Appl. Birkhäuser Boston, vol.22, pp.93-110, 1996.

R. Dautray and J. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, 1985.

D. , D. Silva, and D. Jerison, A singular energy minimizing free boundary. to appear in J, Reine Angew. Math, 2008.

M. C. Delfour and J. Zolésio, Structure of shape derivatives for nonsmooth domains, Journal of Functional Analysis, vol.104, issue.1, pp.1-33, 1992.
DOI : 10.1016/0022-1236(92)90087-Y

M. C. Delfour and J. Zolésio, Shapes and geometries, volume 4 of Advances in Design and Control, Society for Industrial and Applied Mathematics (SIAM) Analysis, 2001.

J. Descloux, A stability result for the magnetic shaping problem, ZAMP Zeitschrift f???r angewandte Mathematik und Physik, vol.21, issue.4, pp.543-555, 1994.
DOI : 10.1007/BF00991896

L. C. Evans and R. F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics, 1992.

H. Federer, Curvature measures, Transactions of the American Mathematical Society, vol.93, issue.3, pp.418-491, 1959.
DOI : 10.1090/S0002-9947-1959-0110078-1

H. Federer, Geometric measure theory. Die Grundlehren der mathematischen Wissenschaften, 1969.

I. Fragalà and F. Gazzola, Partially overdetermined elliptic boundary value problems, Journal of Differential Equations, vol.245, issue.5, pp.1299-1322, 2008.
DOI : 10.1016/j.jde.2008.06.014

I. Fragalà, F. Gazzola, J. Lamboley, and M. Pierre, Counterexamples to symmetry for partially overdetermined elliptic problems. to appear in International mathematical journal of analysis and its applications, 2008.

J. B. Garnett and D. E. Marshall, Harmonic measure, volume 2 of New Mathematical Monographs, 2005.

D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, 2001.

E. Giusti, Minimal surfaces and functions of bounded variation, Monographs in Mathematics, vol.80, 1984.
DOI : 10.1007/978-1-4684-9486-0

J. A. Glaunès, Transport par difféomorphismes de points, de mesures et de courants pour la comparaison de formes et l'anatomie numérique, 2005.

A. Greco and B. Kawohl, On the convexity of some free boundaries, Interfaces and Free Boundaries, 2008.
DOI : 10.4171/IFB/220

P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics, vol.24, 1985.
DOI : 10.1137/1.9781611972030

P. Grisvard, Problèmes aux limites dans des domaines avec points de rebroussement In Partial differential equations and functional analysis, Progr. Nonlinear Differential Equations Appl. Birkhäuser Boston, vol.22, pp.1-17, 1996.

B. Gustafsson and H. Shahgholian, Existence and geometric properties of solutions of a free boundary problem in potential theory, J. Reine Angew. Math, vol.473, pp.137-179, 1996.

J. Hadamard, Mémoire sur un problème d'analyse relatif à l'équilibre des plaques élastiques encastrées. OEuvres de J, pp.515-642, 1908.

M. Hayouni, Sur la minimisation de la premi??re valeur propre du Laplacien, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.330, issue.7, pp.551-556, 2000.
DOI : 10.1016/S0764-4442(00)00229-9

E. Hebey and N. Saintier, Stability and perturbations of the domain for the first eigenvalue of the 1-Laplacian, Archiv der Mathematik, vol.86, issue.4, pp.340-351, 2006.
DOI : 10.1007/s00013-005-1531-7
URL : https://hal.archives-ouvertes.fr/hal-00096407

A. Henrot, Extremum problems for eigenvalues of elliptic operators, Frontiers in Mathematics. Birkhäuser Verlag, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00087731

A. Henrot and E. Oudet, Le stade ne minimise pas parmi les ouverts convexes du plan, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.332, issue.5, pp.417-422, 2001.
DOI : 10.1016/S0764-4442(01)01864-X

A. Henrot and E. Oudet, Minimizing the Second Eigenvalue of the Laplace Operator with Dirichlet Boundary Conditions, Archive for Rational Mechanics and Analysis, vol.169, issue.1, pp.73-87, 2003.
DOI : 10.1007/s00205-003-0259-4
URL : https://hal.archives-ouvertes.fr/hal-00115319

A. Henrot and M. Pierre, Variation et Optimisation de Formes, of Springer Series in Computational Mathematics, 2005.
DOI : 10.1007/3-540-37689-5

A. Henrot, M. Pierre, and M. Rihani, FINITE DIMENSIONAL REDUCTION FOR THE POSITIVITY OF SOME SECOND SHAPE DERIVATIVES, Methods and Applications of Analysis, vol.10, issue.3, pp.457-476, 2003.
DOI : 10.4310/MAA.2003.v10.n3.a7

A. Henrot, M. Pierre, and M. Rihani, Positivity of the Shape Hessian and Instability of some Equilibrium Shapes, Mediterranean Journal of Mathematics, vol.1, issue.2, pp.195-214, 2004.
DOI : 10.1007/s00009-004-0011-9
URL : https://hal.archives-ouvertes.fr/hal-00141917

A. D. Ioffe and V. M. Tihomirov, Theory of extremal problems, Studies in Mathematics and its Applications, 1979.

A. L. Karakhanyan, C. E. Kenig, and H. Shahgholian, The behavior of the free boundary near the fixed boundary for a minimization problem, Calculus of Variations and Partial Differential Equations, vol.9, issue.2, pp.15-31, 2007.
DOI : 10.1007/s00526-006-0029-x

M. Kassmann and W. R. Madych, Difference Quotients and Elliptic Mixed Boundary Problems of Second Order, Indiana University Mathematics Journal, vol.56, issue.3, pp.1047-1082, 2007.
DOI : 10.1512/iumj.2007.56.2836

B. Kawohl and V. Fridman, Isoperimetric estimates for the first eigenvalue of the p-Laplace operator and the Cheeger constant, Comment. Math. Univ. Carolin, vol.44, issue.4, pp.659-667, 2003.

B. Kawohl and T. Lachand-robert, Characterization of Cheeger sets for convex subsets of the plane, Pacific Journal of Mathematics, vol.225, issue.1, pp.103-118, 2006.
DOI : 10.2140/pjm.2006.225.103

D. Kinderlehrer and L. Nirenberg, Regularity in free boundary problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.4, issue.42, pp.373-391, 1977.

Y. Komatu, On starlike and convex mappings of a circle, Kodai Mathematical Seminar Reports, vol.13, issue.2, pp.123-126, 1961.
DOI : 10.2996/kmj/1138844403

T. Lachand-robert, Minimization sous contraintes de convexité ou globales

T. Lachand-robert and E. Oudet, Minimizing within Convex Bodies Using a Convex Hull Method, SIAM Journal on Optimization, vol.16, issue.2, pp.368-379, 2005.
DOI : 10.1137/040608039
URL : https://hal.archives-ouvertes.fr/hal-00385109

T. Lachand-robert and M. A. Peletier, An example of non-convex minimization and an application to Newton's problem of the body of least resistance, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.18, issue.2, pp.179-198, 2001.
DOI : 10.1016/S0294-1449(00)00062-7

T. Lachand-robert and M. A. Peletier, Newton's Problem of the Body of Minimal Resistance in the Class of Convex Developable Functions, Mathematische Nachrichten, vol.173, issue.1, pp.153-176, 2001.
DOI : 10.1002/1522-2616(200106)226:1<153::AID-MANA153>3.0.CO;2-2

J. Lamboley, About hölder-regularity of the optimal convex shape for ? 2 . in preparation, 2008.

J. Lamboley and A. Novruzi, Polygons as optimal shapes with convexity constraint. soumis, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00362329

J. Lamboley and M. Pierre, Structure of shape derivatives around irregular domains and applications, J. Convex Anal, vol.14, issue.4, pp.807-822, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00095949

N. Landais, Problèmes de régularité en Optimisation de Forme, Thèse de l'ENS Cachan, 2007.

N. Landais, A regularity result in a shape optimization problem with perimeter, J. Convex Anal, vol.14, issue.4, pp.785-806, 2007.

D. Lanphier and J. Rosenhouse, Lower bounds on the Cheeger constants of highly connected regular graphs, 36th Southeastern International Conference on Combinatorics, Graph Theory, and Computing, pp.65-74, 2005.

M. Lanza-de-cristoforis, A note on conformal representation in Sobolev spaces. Complex Variables Theory Appl, pp.121-133, 1992.

A. Laurain, Structure of shape derivatives in nonsmooth domains and applications, Adv. Math. Sci. Appl, vol.15, issue.1, pp.199-226, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00139059

A. Laurain, Domaines singulièrement perturbés en optimisation de formes, Thèse de l'université H. Poincaré Nancy 1, 2006.

P. Lions, The concentration-compactness principle in the Calculus of Variations. The locally compact case, part 1. * *Mp denotes the Marcinkiewicz space or weak Lp space, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.1, issue.2, pp.109-145, 1984.
DOI : 10.1016/S0294-1449(16)30428-0

A. Mannino, Some inequalities concerning starlike and convex functions, Gen. Math, vol.12, issue.1, pp.5-12, 2004.

A. Marx, Untersuchungen ???ber schlichte Abbildungen, Mathematische Annalen, vol.17, issue.1, pp.40-67, 1933.
DOI : 10.1007/BF01448878

N. Matevosyan, Tangential Touch Between Free and Fixed Boundaries in a Problem from Superconductivity, Communications in Partial Differential Equations, vol.101, issue.8, pp.1205-1216, 2005.
DOI : 10.1215/S0012-7094-03-11611-7

H. Maurer and J. Zowe, First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems, Mathematical Programming, vol.15, issue.1, 1979.
DOI : 10.1007/BF01582096

V. G. Maz-'ya and B. A. Plamenevskii, Estimates in L p and in Hölder classes and the Miranda- Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary, Amer. Math. Soc. Transl, vol.123, issue.2, pp.1-56, 1984.

A. D. Melas, On the nodal line of the second eigenfunction of the Laplacian in $\mathbf{R}^2$, Journal of Differential Geometry, vol.35, issue.1, pp.255-263, 1992.
DOI : 10.4310/jdg/1214447811

D. Mitrea and I. Mitrea, On the Besov regularity of conformal maps and layer potentials on nonsmooth domains, Journal of Functional Analysis, vol.201, issue.2, pp.380-429, 2003.
DOI : 10.1016/S0022-1236(03)00086-7

I. Mitrea and M. Mitrea, The Poisson problem with mixed boundary conditions in Sobolev and Besov spaces in non-smooth domains, Transactions of the American Mathematical Society, vol.359, issue.09, pp.4143-4182, 2007.
DOI : 10.1090/S0002-9947-07-04146-3

J. Morvan, Generalized Curvatures, volume 2 of Geometry and Computing, 2008.

A. Novruzi and M. Pierre, Structure of shape derivatives, Journal of Evolution Equations, vol.2, issue.3, pp.365-382, 2002.
DOI : 10.1007/s00028-002-8093-y

E. Oudet, Quelques résultats en optimisation de forme et stabilisation

E. Oudet, Numerical minimization of eigenmodes of a membrane with respect to the domain, ESAIM: Control, Optimisation and Calculus of Variations, vol.10, issue.3, pp.315-330, 2004.
DOI : 10.1051/cocv:2004011
URL : https://hal.archives-ouvertes.fr/hal-00384996

C. Pommerenke, Boundary behaviour of conformal maps, 1992.
DOI : 10.1007/978-3-662-02770-7

J. Prajapat, Serrin's result for domains with a corner or cusp. Duke Math, J, vol.91, issue.1, pp.29-31, 1998.

L. Roques and F. Hamel, Mathematical analysis of the optimal habitat configurations for species persistence, Mathematical Biosciences, vol.210, issue.1, pp.34-59, 2007.
DOI : 10.1016/j.mbs.2007.05.007
URL : https://hal.archives-ouvertes.fr/hal-00149538

G. Savaré, Regularity and perturbation results for mixed second order elliptic problems, Communications in Partial Differential Equations, vol.22, issue.6, pp.869-899, 1997.
DOI : 10.1080/03605309708821287

C. Scheid, Analyse théorique et numérique au voisinage du point triple en électromouillage, 2007.

C. Scheid and P. Witomski, A proof of the invariance of the contact angle in electrowetting, Mathematical and Computer Modelling, vol.49, issue.3-4, 2008.
DOI : 10.1016/j.mcm.2008.01.009
URL : https://hal.archives-ouvertes.fr/hal-00388188

J. Serrin, A symmetry problem in potential theory, Archive for Rational Mechanics and Analysis, vol.43, issue.4, pp.304-318, 1971.
DOI : 10.1007/BF00250468

H. Shahgholian and N. Uraltseva, Regularity properties of a free boundary near contact points with the fixed boundary, Duke Math. J, vol.116, issue.1, pp.1-34, 2003.

H. Shahgholian and G. S. Weiss, The two-phase membrane problem???An intersection-comparison approach to the regularity at branch points, Advances in Mathematics, vol.205, issue.2, pp.487-503, 2006.
DOI : 10.1016/j.aim.2005.07.015

E. Shamir, Regularization of mixed second-order elliptic problems, Israel Journal of Mathematics, vol.67, issue.2, pp.150-168, 1968.
DOI : 10.1007/BF02760180

L. Simon, Lectures on geometric measure theory, of Proceedings of the Centre for Mathematical Analysis, 1983.

J. Simons, Minimal Varieties in Riemannian Manifolds, The Annals of Mathematics, vol.88, issue.1, pp.62-105, 1968.
DOI : 10.2307/1970556

J. Soko?owski and J. Zolésio, Introduction to shape optimization, of Springer Series in Computational Mathematics, 1992.

G. Strang, Maximum area with Minkowski measures of perimeter, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.138, issue.01, pp.189-199, 2008.
DOI : 10.1017/S0308210506000862

E. Stredulinsky and W. P. Ziemer, Area minimizing sets subject to a volume constraint in a convex set, Journal of Geometric Analysis, vol.334, issue.4, pp.653-677, 1997.
DOI : 10.1007/BF02921639

E. Strohhäcker, Beitr???ge zur Theorie der schlichten Funktionen, Mathematische Zeitschrift, vol.37, issue.1, pp.356-380, 1933.
DOI : 10.1007/BF01474580

V. ?verák, On optimal shape design, J. Math. Pures Appl, vol.72, issue.96, pp.537-551, 1993.

N. Van-goethem, Variational problems on classes of convex domains, Commun. Appl. Anal, vol.8, issue.3, pp.353-371, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00137953

A. L. Vogel, Symmetry and regularity for general regions having a solution to certain overdetermined boundary value problems, Atti Sem. Mat. Fis. Univ. Modena, vol.40, issue.2, pp.443-484, 1992.

A. Wagner, Optimal Shape Problems for Eigenvalues, Communications in Partial Differential Equations, vol.23, issue.7, pp.1039-1063, 2005.
DOI : 10.1007/BF01208645

S. E. Warschawski, On differentiability at the boundary in conformal mapping, Proc. Amer, pp.614-620, 1961.
DOI : 10.1090/S0002-9939-1961-0131524-8

G. S. Weiss, Partial regularity for weak solutions of an elliptic free boundary problem, Communications in Partial Differential Equations, vol.966, issue.3-4, pp.439-455, 1998.
DOI : 10.1007/BF01165828

G. S. Weiss, Partial regularity for a minimum problem with free boundary, Journal of Geometric Analysis, vol.325, issue.2, pp.317-326, 1999.
DOI : 10.1007/BF02921941

N. M. Wigley, Schauder estimates in domains with corners, Archive for Rational Mechanics and Analysis, vol.24, issue.2, pp.271-276, 1988.
DOI : 10.1007/BF00281357