A maximum principle for some fully nonlinear elliptic equations with applications to Weingarten hypersurfaces

DOI10.1080/17476933.2012.712966zbMath1277.35085OpenAlexW2062714236MaRDI QIDQ2862987

Cristian Enache, Luminita Barbu

Publication date: 20 November 2013

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2012.712966

zbMATH Keywords

Weingarten hypersurfacesHopf's first maximum principle

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45)

Related Items (5)

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 ⋮ 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

Cites Work

• Maximum principles and symmetry results for a class of fully nonlinear elliptic PDEs
• Best possible maximum principles for fully nonlinear elliptic partial differential equations
• The convexity of solution of a class Hessian equation in bounded convex domain in \(\mathbb R^3\)
• Serrin-type overdetermined problems: An alternative proof
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• On the Dirichlet problem for Hessian equations
• Variational properties of functions of the mean curvatures for hypersurfaces in space forms
• Some applications of the maximum principle to a variety of fully nonlinear elliptic PDE's
• A Brunn-Minkowski inequality for the Hessian eigenvalue in three-dimensional convex domain
• Nonlinear second-order elliptic equations V. The dirichlet problem for weingarten hypersurfaces
• Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature
• SOME MAXIMUM PRINCIPLES AND SYMMETRY RESULTS FOR A CLASS OF BOUNDARY VALUE PROBLEMS INVOLVING THE MONGE-AMPÈRE EQUATION

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