The nonhomogeneous minimal surface equation involving a measure
type: Item
instance of: scholarly article
title: The nonhomogeneous minimal surface equation involving a measure
zbMATH Open document ID: 0820.49018
author: William K. Ziemer
published in: Pacific Journal of Mathematics
publication date: 1995-08-29T00:00:00Z
review text: We find existence of a minimum in BV for the variational problem associated with \(\text{div } A(Du)+ \mu= 0\), where \(A\) is a mean curvature type operator and \(\mu\) a nonnegative measure satisfying a suitable growth condition. We then show a local \(L^ \infty\) estimate for the minimum. A similar local \(L^ \infty\) estimate is shown for sub- solutions that are Sobolev rather than BV.
Mathematics Subject Classification ID: 49Q05
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 759258
zbMATH Keywords: minimal surface equation
zbMATH Keywords: variational solution
zbMATH Keywords: nonlinear elliptic partial differential equations
zbMATH Keywords: local bound solution
MaRDI profile type: Publication
full work available at URL: pjm.1995.167.183
OpenAlex ID: W1991155257
DOI: 10.2140/PJM.1995.167.183
description: scientific article; zbMATH DE number 759258