On the behavior of a non-parametric minimal surface in a non-convex quadrilateral
type: Item
instance of: scholarly article
title: On the behavior of a non-parametric minimal surface in a non-convex quadrilateral
zbMATH Open document ID: 0619.49018
DOI: 10.1007/BF00279863
author: A. Elcrat
author: Kirk E. Lancaster
published in: Archive for Rational Mechanics and Analysis
publication date: 1986-01-01T00:00:00Z
review text: The boundary behaviour of generalized solutions of the Dirichlet problem for the minimal surface equation is studied. In particular the special case of a nonconvex quadrilateral is considered by the authors. In this case the only point of interest is the behaviour of the solution at the reentrant corner of the domain. It is known since some time, that for special senseful boundary values a classical solution of the boundary value problem does not exist. But weak solutions in the usual setting exist. It is shown that the generalized solution may be thought as the solution of an obstacle problem.
Mathematics Subject Classification ID: 49Q05
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35J85
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 4005029
zbMATH Keywords: boundary behaviour
zbMATH Keywords: generalized solutions
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: minimal surface equation
zbMATH Keywords: nonconvex quadrilateral
zbMATH Keywords: obstacle problem
reviewed by: G. Dziuk
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4005029