Best possible maximum principles for fully nonlinear elliptic partial differential equations
type: Item
instance of: scholarly article
title: Best possible maximum principles for fully nonlinear elliptic partial differential equations
zbMATH Open document ID: 1236.35015
DOI: 10.4171/ZAA/1299
author: Giovanni Porru
author: Abdessalam Safoui
author: Stella Vernier Piro
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2007-03-20T00:00:00Z
review text: Summary: We investigate a class of equations including generalized Monge--Ampère equations as well as Weingarten equations and prove a maximum principle for suitable functions involving the solution and its gradient. Since the functions which enjoy the maximum principles are constant for special domains, we have a so called best possible maximum principle that can be used to find accurate estimates for the solution of the corresponding Dirichlet problem. For these equations we also give a variational form which may have its own interest.
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 35J96
zbMATH DE Number: 5135096
zbMATH Keywords: fully nonlinear elliptic equations, Weingarten surfaces, best possible maximum principles
MaRDI profile type: Publication
cites work: The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
cites work: Nonlinear second-order elliptic equations V. The dirichlet problem for weingarten hypersurfaces
cites work: Elliptic Partial Differential Equations of Second Order
cites work: Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature
cites work: SOME MAXIMUM PRINCIPLES AND SYMMETRY RESULTS FOR A CLASS OF BOUNDARY VALUE PROBLEMS INVOLVING THE MONGE-AMPÈRE EQUATION
full work available at URL: https://doi.org/10.4171/zaa/1299
OpenAlex ID: W2094477957
description: scientific article; zbMATH DE number 5135096