Maximum principles and symmetry results for a class of fully nonlinear elliptic PDEs

DOI10.1007/s00030-010-0070-5zbMath1200.35113OpenAlexW1985413881MaRDI QIDQ601745

Cristian Enache

Publication date: 29 October 2010

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-010-0070-5

zbMATH Keywords

a priori boundsmaximum principlesradial solutionsfully nonlinear elliptic equationsoverdetermined problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Free boundary problems for PDEs (35R35)

Related Items (9)

An extension of maximum principle with some applications ⋮ Maximum principles and overdetermined problems for Hessian equations ⋮ Maximum principles and isoperimetric inequalities for some Monge-Ampère-type problems ⋮ Maximum and minimum principles for a class of Monge-Ampère equations in the plane, with applications to surfaces of constant Gauss curvature ⋮ Overdetermined problems for fully nonlinear elliptic equations ⋮ A note on Monge-Ampère equation in \(\mathbb{R}^2\) ⋮ Necessary conditions of solvability and isoperimetric estimates for some Monge-Ampère problems in the plane ⋮ A maximum principle for some fully nonlinear elliptic equations with applications to Weingarten hypersurfaces ⋮ A sharp global estimate and an overdetermined problem for Monge-Ampère type equations

Cites Work

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• On the Dirichlet problem for Hessian equations
• Some applications of the maximum principle to a variety of fully nonlinear elliptic PDE's
• A symmetry problem in potential theory
• On the Hessian of a function and the curvature of its graph
• Symmetry Theorems Related to Pompeiu's Problem
• Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature
• A necessary condition of solvability for the capillarity boundary of Monge-Ampere equations in two dimensions
• On new isoperimetric inequalities and symmetrization.
• SOME MAXIMUM PRINCIPLES AND SYMMETRY RESULTS FOR A CLASS OF BOUNDARY VALUE PROBLEMS INVOLVING THE MONGE-AMPÈRE EQUATION

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