Nonlinear second-order elliptic equations with jump discontinuous coefficients. I: Quasilinear equations
type: Item
instance of: scholarly article
title: Nonlinear second-order elliptic equations with jump discontinuous coefficients. I: Quasilinear equations
zbMATH Open document ID: 0785.35037
published in: Differential and Integral Equations
publication date: 1993-01-16T00:00:00Z
review text: The paper is the first in a series of two, dealing with the Dirichlet problem for quasilinear and fully nonlinear uniformly elliptic equations with coefficients with a possible jump along a surface and smooth on both sides of it. This first paper treats the quasilinear case. The authors formulate some uniqueness results (valid also for fully nonlinear equations). Then they regularize the given equation by using a suitable cut-off function and replacing the elliptic operator by the Laplacian in a neighborhood of the surface. Suitable a priori estimates and the Cantor diagonalization process provide the convergence of the classical solutions of the regularized problems to a weak solution of the original one.
reviewed by: J.Madjarova
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 94949
zbMATH Keywords: quasilinear elliptic equations
zbMATH Keywords: discontinuous coefficients
zbMATH Keywords: regularization
zbMATH Keywords: convergence to weak solution
zbMATH Keywords: a priori estimates
zbMATH Keywords: Cantor diagonalization process
author: N. Kutev
author: P.-L. Lions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 94949