A Green's formula for quasilinear elliptic operators
type: Item
instance of: scholarly article
title: A Green's formula for quasilinear elliptic operators
zbMATH Open document ID: 0704.35047
DOI: 10.1016/0022-247X(89)90164-9
author: Eduardo Casas
author: Luis Alberto Fernández
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: The authors consider the Neumann problem (with conormal derivative given) for a quasilinear second order elliptic equation \(Au=f\) in \(\Omega\) in divergence form. Here \(\Omega\) is a bounded domain with Lipschitz boundary. If A is linear it is well known that once \(Au\in L^ 2(\Omega)\) and \(u\in W^{1,2}(\Omega)\), then \(\partial u/\partial n_ A\) is well defined in \(W^{-1/2,2}\). For quasilinear A, for \(u\in W^{1,p}(\Omega)\) and \(Au\in L^ 1(\Omega)\) (resp. \(Au\in L^ q(\Omega))\) the authors derive the natural spaces in which \(\partial u/\partial n_ A\) lies and prove a Green's formula.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 26B20
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 4154997
zbMATH Keywords: Green's formula
zbMATH Keywords: trace theorem
zbMATH Keywords: Neumann problem
zbMATH Keywords: divergence form
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4154997