Nonparametric minimal surfaces in \(R^ 3\) whose boundaries have a jump discontinuity
type: Item
instance of: scholarly article
title: Nonparametric minimal surfaces in \(R^ 3\) whose boundaries have a jump discontinuity
zbMATH Open document ID: 0696.35057
DOI: 10.1155/S0161171288000791
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46453
review text: Summary: Let \(\Omega\) be a domain in \({\mathbb{R}}^ 2\) which is locally convex at each point of its boundary except possibly one, say (0,0), \(\phi\) be continuous on \(\partial \Omega /\{(0,0)\}\) with a jump discontinuity at (0,0) and f be the unique variational solution of the minimal surface equation with boundary values \(\phi\). Then the radial limits of f at (0,0) from all directions in \(\Omega\) exist. If the radial limits all lie between the lower and upper limits of \(\phi\) at (0,0), then the radial limits of f are weakly monotonic; if not, they are weakly increasing and then decreasing (or the reverse). Additionally, their behavior near the extreme directions is examined and a conjecture of the author is proven.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35J67
Mathematics Subject Classification ID: 49Q05
zbMATH DE Number: 4140287
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: nonparametric minimal surfaces
zbMATH Keywords: variational solution
author: Kirk E. Lancaster
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4140287