The prescribed mean curvature equation for nonparametric surfaces
type: Item
instance of: scholarly article
title: The prescribed mean curvature equation for nonparametric surfaces
zbMATH Open document ID: 1029.53070
DOI: 10.1016/S0362-546X(02)00105-0
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: Consider the Dirichlet problem in a bounded \(C^{1,1}\) domain \(\Omega \subset \mathbb{R}^n\), for an embedded surface given by the graph of a function \(u:\overline {\Omega} \to R\), for the prescribed mean curvature equation: \({\text div} ({\nabla u \over \sqrt{1 +|\nabla u|^2}})=nH(x,u)\) in \(\Omega\) and \(u=g\) in \(\partial \Omega\). The authors obtain existence and uniqueness results in the Sobolev space \(W^{2,p}\). Moreover, under appropriate conditions, it is proved that the set of surfaces with mean curvature \(H\) is a connected subset of \(W^{2,p}\).
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 1879997
zbMATH Keywords: nonparametric surface
zbMATH Keywords: prescribed mean curvature equation
zbMATH Keywords: Sobolev space
author: Pablo Amster
author: Maria C. Mariani
reviewed by: Thomas Hasanis
MaRDI profile type: Publication
cites work: The prescribed mean curvature equation with Dirichlet conditions
cites work: Existence and uniqueness of \(H\)-system's solutions with Dirichlet conditions
cites work: Multiple solutions ofH-systems and Rellich's conjecture
cites work: Q4040640
cites work: On the plateau problem for surfaces of constant mean curvature
cites work: A Dirichlet problem for an \(H\)-system with variable \(H\)
cites work: Solutions to the mean curvature equation by fixed point methods
cites work: Q4692400
cites work: Q3482498
cites work: The Dirichlet problem for the equation of prescribed mean curvature
full work available at URL: s0362-546x(02)00105-0
OpenAlex ID: W2015962933
description: scientific article; zbMATH DE number 1879997