Some existence results for operator equations involving duality mappings on Sobolev spaces with variable exponent
type: Item
instance of: scholarly article
title: Some existence results for operator equations involving duality mappings on Sobolev spaces with variable exponent
zbMATH Open document ID: 1240.46062
published in: Differential and Integral Equations
publication date: 2011-09-01T00:00:00Z
review text: The authors consider duality equations \(J_{\varphi }u=h\) and \(J_{\varphi }u=N_{f}u\) in variable exponent Sobolev spaces on some domain \(\varOmega \), where \(J_{\varphi }\) and \(N_{f}\) is a duality mapping with gauge \(\varphi \) and the Nemytskii operator generated by a Carathéodory function \(f\), respectively. Surjectivity results are established under suitable additional assumptions on the smoothness of \(\varOmega \) and growth conditions on \(f\) linked with the variable exponents in question. The major tools, also established here, are smoothness properties of the norm. A formula for the gradient of the norm is proved.
reviewed by: Miroslav Krbec
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 46G05
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 5944856
zbMATH Keywords: Lebesgue space
zbMATH Keywords: Sobolev space
zbMATH Keywords: variable exponent
zbMATH Keywords: duality mapping
zbMATH Keywords: smoothness of norms
zbMATH Keywords: reflexivity
author: George Dinca
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5944856