Solutions to \(H\)-systems by topological and iterative methods
type: Item
instance of: scholarly article
title: Solutions to \(H\)-systems by topological and iterative methods
zbMATH Open document ID: 1163.35390
DOI: 10.1155/S1085337503209015
published in: Abstract and Applied Analysis
publication date: 2003-06-18T00:00:00Z
full work available at URL: https://eudml.org/doc/55533
review text: The authors consider the Dirichlet problem in a bounded \(C^{1,1}\) domain \(\Omega\subset\mathbb R^2\) for a vector function \(X:\overline{\Omega}\to\mathbb R^3\) which satisfies the equation of prescribed mean curvature \[ \Delta X= 2H(u,\nu,X)X_u\wedge X_\nu \quad\text{in }\Omega, \qquad X=g \quad\text{on }\partial\Omega, \tag{1} \] where \(\wedge\) denotes the exterior product in \(\mathbb R^3\), \(H:\overline{\Omega}\times\mathbb R^3\to\mathbb R\) is a given continuous function, and the boundary data \(g\) is smooth. Under some natural assumptions on \(g\) and \(H\), the authors show, a map generated by (1) is an open map, that is if (1) admits a solution for some \((H_0,g_0)\), then (1) is solvable for any \((H,g)\) close enough to \((H_0,g_0)\) as well. To this end, they use a Newton iteration.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 1929997
zbMATH Keywords: topological and iterative theorems
zbMATH Keywords: equation of prescribed mean curvature
author: Pablo Amster
author: Maria C. Mariani
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
OpenAlex ID: W1989538186
description: scientific article; zbMATH DE number 1929997