NONLINEAR POTENTIAL THEORY AND QUASILINEAR EQUATIONS WITH MEASURE DATA

Abstract : This thesis is concerned to the existence and regularity of solutions to nonlinear elliptic, parabolic and Hessian equations with measure, and criteria for the existence of large solutions to some nonlinear elliptic and parabolic equations. \\\\ \textbf{List of preprints and publications in this thesis} \begin{description} \item[1.] With M. F. Bidaut-Véron, L. Véron; {\em Quasilinear Lane-Emden equations with absorption and measure data,} Journal des Mathématiques Pures et Appliquées, {\bf 102}, 315-337 (2014). \item[2] With L. Véron; {\em Quasilinear and Hessian type equations with exponential reaction and measure data,} Archive for Rational Mechanics and Analysis, {\bf 214}, 235-267 (2014). \item[3] With L. Véron; {\em Wiener criteria for existence of large solutions of quasilinear elliptic equations with absorption,} 17 pages, Submitted, arXiv:1308.2956. \item[4] With M. F. Bidaut-Véron; {\em Stability properties for quasilinear parabolic equations with measure data,} 29 pages, to appear in Journal of European Mathematical Society, arXiv:1409.1518. \item[5] Avec M. F. Bidaut-Véron; {\em Evolution equations of $p$-Laplace type with absorption or source terms and measure data}, 21 pages, to appear in Communications in Contemporary Mathematics, arXiv:1409.1520. \item[6] {\em Potential estimates and quasilinear parabolic equations with measure data,} 118 pages, arXiv:1405.2587v1. \item[7] With L. Véron; {\em Wiener criteria for existence of large solutions of nonlinear parabolic equations with absorption in a non-cylindrical domain,} 29 pages, submitted,\\ arXiv:1406.3850. \item[8] With M. F. Bidaut-Véron; {Pointwise estimates and existence of solutions of porous medium and $p$-Laplace evolution equations with absorption and measure data,\em } 27 pages, submitted, arXiv:1407.2218. \end{description}
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Submitted on : Friday, September 12, 2014 - 3:45:07 PM
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• HAL Id : tel-01063365, version 1

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Quoc-Hung Nguyen. NONLINEAR POTENTIAL THEORY AND QUASILINEAR EQUATIONS WITH MEASURE DATA. Analysis of PDEs [math.AP]. Université François Rabelais - Tours, 2014. English. ⟨tel-01063365⟩

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