Lectures on exponential decay of solutions of second-order elliptic equations : bounds on eigenfunctions of N body Schrödinger operators, Schrödinger operators, pp.1-38, 1965. ,
DOI : 10.1515/9781400853076
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Communications on Pure and Applied Mathematics, vol.29, issue.4, pp.623-727, 1959. ,
DOI : 10.1002/cpa.3160120405
Analyse num??rique de la supraconductivit??, Comptes Rendus Mathematique, vol.337, issue.8, pp.543-548, 2003. ,
DOI : 10.1016/j.crma.2003.09.007
Energy and vorticity of the Ginzburg???Landau model with variable magnetic field, Asymptotic Analysis, vol.93, issue.1-2, pp.75-114, 2015. ,
DOI : 10.3233/ASY-151286
Schrödinger operators with magnetic fields. I. General interactions, Duke Math, J, vol.45, pp.847-883, 1978. ,
Stable Nucleation for the Ginzburg-Landau System with an Applied Magnetic Field, Archive for Rational Mechanics and Analysis, vol.142, issue.1, pp.1-43, 1998. ,
DOI : 10.1007/s002050050082
An application of semi-classical analysis to the asymptotic study of the supercooling field of a superconducting material, Ann. Inst. H. Poincaré Phys. Théor, vol.58, pp.189-233, 1993. ,
The Ginzburg-Landau equations in a semi-infinite superconducting film in the large ? limit, European J. Appl. Math, vol.8, pp.347-367, 1997. ,
On the fundamental state energy for a Schrödinger operator with magnetic field in domains with corners, Asymptot. Anal, vol.41, pp.215-258, 2005. ,
Harmonic oscillators with Neumann condition on the half-line, Communications on Pure and Applied Analysis, vol.11, issue.6, pp.2221-2237, 2012. ,
DOI : 10.3934/cpaa.2012.11.2221
Asymptotics for the low-lying eigenstates of the Schrödinger operator with magnetic field near corners, pp.899-931, 2006. ,
Computations of the first eigenpairs for the Schr??dinger operator with magnetic field, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.37-40, pp.3841-3858, 2007. ,
DOI : 10.1016/j.cma.2006.10.041
Ground state energy of the magnetic Laplacian on corner domains , ArXiv e-prints, 2014. ,
SUPERCONDUCTIVITY IN DOMAINS WITH CORNERS, Reviews in Mathematical Physics, vol.19, issue.06, pp.607-637, 2007. ,
DOI : 10.1142/S0129055X07003061
Magnetic WKB Constructions, Archive for Rational Mechanics and Analysis, vol.12, issue.14, pp.817-891, 2016. ,
DOI : 10.1007/s00205-016-0987-x
Breaking a magnetic zero locus: model operators and numerical approach, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.8, issue.10, pp.120-139, 2015. ,
DOI : 10.1002/zamm.201300086
Functional analysis, Sobolev spaces and partial differential equations, 2011. ,
DOI : 10.1007/978-0-387-70914-7
Schrödinger operators with application to quantum mechanics and global geometry, Texts and Monographs in Physics, 1987. ,
Eigenvalues Variation. I., Journal of Differential Equations, vol.104, issue.2, pp.243-262, 1993. ,
DOI : 10.1006/jdeq.1993.1071
Boundary Concentration for Eigenvalue Problems Related to the Onset of Superconductivity, Communications in Mathematical Physics, vol.210, issue.2, pp.413-446, 2000. ,
DOI : 10.1007/s002200050786
Semiclassical analysis with vanishing magnetic fields, Journal of Spectral Theory, vol.3, issue.3, pp.423-464, 2013. ,
DOI : 10.4171/JST/50
Estimations asymptotiques pr??cises pour le laplacien magn??tique de Neumann, Annales de l???institut Fourier, vol.56, issue.1, pp.1-67, 2006. ,
DOI : 10.5802/aif.2171
Spectral methods in surface superconductivity, Progress in Nonlinear Differential Equations and their Applications, 2010. ,
DOI : 10.1007/978-0-8176-4797-1
Strong diamagnetism for the ball in three dimensions, Asymptot. Anal, vol.72, pp.77-123, 2011. ,
A uniqueness theorem for higher order anharmonic oscillators, Journal of Spectral Theory, vol.5, issue.2, pp.235-249, 2015. ,
DOI : 10.4171/JST/96
Dirichlet's problem for linear elliptic partial differential equations, MATHEMATICA SCANDINAVICA, vol.1, pp.55-72, 1953. ,
DOI : 10.7146/math.scand.a-10364
Semi-classical analysis for the Schrödinger operator and applications, Lecture Notes in Mathematics, vol.1336, 1988. ,
The Montgomery model revisited, Colloquium Mathematicum, vol.118, issue.2, pp.391-400, 2010. ,
DOI : 10.4064/cm118-2-3
Magnetic Wells in Dimension Three. working paper or preprint, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01149246
Spectral gaps for periodic Schr??dinger operators with hypersurface magnetic wells: Analysis near the bottom, Journal of Functional Analysis, vol.257, issue.10, pp.3043-3081, 2009. ,
DOI : 10.1016/j.jfa.2009.04.007
Semiclassical spectral asymptotics for a two-dimensional magnetic Schr??dinger operator: The case of discrete wells, Contemp. Math., Amer. Math. Soc, vol.535, pp.55-78, 2011. ,
DOI : 10.1090/conm/535/10535
Caract??risation du spectre essentiel de l'op??rateur de Schr??dinger avec un champ magn??tique, Annales de l???institut Fourier, vol.38, issue.2, pp.95-112, 1988. ,
DOI : 10.5802/aif.1136
Semiclassical Analysis for the Ground State Energy of a Schr??dinger Operator with Magnetic Wells, Journal of Functional Analysis, vol.138, issue.1, pp.40-81, 1996. ,
DOI : 10.1006/jfan.1996.0056
Magnetic Bottles in Connection with Superconductivity, Journal of Functional Analysis, vol.185, issue.2, pp.604-680, 2001. ,
DOI : 10.1006/jfan.2001.3773
Magnetic bottles for the Neumann problem: curvature effects in the case of dimension 3 (general case), Annales Scientifiques de l?????cole Normale Sup??rieure, vol.37, issue.1, pp.37-105, 2004. ,
DOI : 10.1016/j.ansens.2003.04.003
Hypoellipticit?? maximale pour des op??rateurs polyn??mes de champs de vecteurs, Journ??es ??quations aux d??riv??es partielles, vol.58, 1985. ,
DOI : 10.5802/jedp.206
Reduced Landau???de Gennes functional and surface smectic state of liquid crystals, Journal of Functional Analysis, vol.255, issue.11, pp.3008-3069, 2008. ,
DOI : 10.1016/j.jfa.2008.04.011
Spectral properties of higher order anharmonic oscillators, Journal of Mathematical Sciences, vol.28, issue.3, pp.165-110, 2010. ,
DOI : 10.1007/s10958-010-9784-5
Multiple wells in the semi-classical limit I, Communications in Partial Differential Equations, vol.52, issue.2, pp.337-408, 1984. ,
DOI : 10.1080/03605308408820335
Perturbation Theory for Linear Operators [51] , Perturbation theory for linear operators, Classics in Mathematics, 1966. ,
Hyperbolic differential equations, The Institute for Advanced Study, 1953. ,
Eigenvalue problems of Ginzburg-Landau operator in bounded domains, J. Math. Phys, vol.40, pp.2647-2670, 1999. ,
Introduction à la théorie spectrale -Cours et exercices corrigés, 2003. ,
Hearing the zero locus of a magnetic field, Communications in Mathematical Physics, vol.3, issue.np. 3, pp.651-675, 1995. ,
DOI : 10.1007/BF02101848
Surface superconductivity in 3 dimensions, Transactions of the American Mathematical Society, vol.356, issue.10, pp.3899-3937, 2004. ,
DOI : 10.1090/S0002-9947-04-03530-5
Schrödinger operators with non-degenerately vanishing magnetic fields in bounded domains, Trans. Amer. Math. Soc, vol.354, pp.4201-4227, 2002. ,
Bounds for the Discrete Part of the Spectrum of a Semi-Bounded Schr??dinger Operator., MATHEMATICA SCANDINAVICA, vol.8, pp.143-153, 1960. ,
DOI : 10.7146/math.scand.a-10602
When the 3D Magnetic Laplacian Meets a Curved Edge in the Semiclassical Limit, SIAM Journal on Mathematical Analysis, vol.45, issue.4, pp.2354-2395, 2013. ,
DOI : 10.1137/130906003
URL : https://hal.archives-ouvertes.fr/hal-00746862
Sharp Asymptotics for the Neumann Laplacian with Variable Magnetic Field: Case of Dimension 2, Annales Henri Poincar??, vol.10, issue.1, pp.95-122, 2009. ,
DOI : 10.1007/s00023-009-0405-0
Breaking a magnetic zero locus: Asymptotic analysis, Mathematical Models and Methods in Applied Sciences, vol.24, issue.14, pp.2785-2817, 2014. ,
DOI : 10.1142/S0218202514500377
URL : https://hal.archives-ouvertes.fr/hal-00790439
Semiclassical analysis of low lying eigenvalues. I. Nondegenerate minima : asymptotic expansions, pp.38-295, 1983. ,