Existence and uniqueness of \(H\)-system's solutions with Dirichlet conditions
type: Item
instance of: scholarly article
title: Existence and uniqueness of \(H\)-system's solutions with Dirichlet conditions
zbMATH Open document ID: 0968.53006
DOI: 10.1016/S0362-546X(99)00123-6
author: Diego F. Rial
author: Pablo Amster
author: Maria C. Mariani
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2000-10-23T00:00:00Z
review text: Let \(B= \{(u, v)\in \mathbb{R}^2\mid u^2+ v^2< 1\}\) be the unit disc. The main purpose of this paper is to find a vector function \(u:\overline B\to \mathbb{R}^3\) satisfying the prescribed mean curvature equation \(\Delta X= 2H(u,v) X_u\wedge X_v\) in \(B\), and \(X= g\) on \(\partial B\), where \(\wedge\) denotes the exterior product and \(H:\overline B\to\mathbb{R}\) is a given continuous function, while \(g\) is in a Sobolev space \(W^{2,p}(B, \mathbb{R}^3)\). Using Sobolev immersion the authors transform the above problem into a contraction mapping on the Sobolev space \(W^{1,p}\), and then derive the existence and local uniqueness for a solution of the mean curvature equation.
reviewed by: Fuliu Zhu
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1513367
zbMATH Keywords: prescribed mean curvature equation
zbMATH Keywords: Sobolev space
MaRDI profile type: Publication
full work available at URL: s0362-546x(99)00123-6
OpenAlex ID: W2015601628
description: scientific article; zbMATH DE number 1513367