Nonlocal Variational Principles with Variable Growth

Nonlocal Variational Principles with Variable Growth

This paper is concerned with the functional J defined by J(u)=∫Ω×ΩW(x,y,∇u(x),∇u(y))dx dy, where Ω⊂ℝN is a regular open bounded set and W is a real-valued function with variable growth. After discussing the theory of Young measures in variable exponent Sobolev spaces, we study the weak lower semicon...

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Main Authors: Yongqiang Fu, Miaomiao Yang
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2014/435247
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spelling doaj-b0aa2291c3a54604bad0a79bd854558d2020-11-24T22:35:42ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/435247435247Nonlocal Variational Principles with Variable GrowthYongqiang Fu0Miaomiao Yang1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaThis paper is concerned with the functional J defined by J(u)=∫Ω×ΩW(x,y,∇u(x),∇u(y))dx dy, where Ω⊂ℝN is a regular open bounded set and W is a real-valued function with variable growth. After discussing the theory of Young measures in variable exponent Sobolev spaces, we study the weak lower semicontinuity and relaxation of J.http://dx.doi.org/10.1155/2014/435247
collection DOAJ
language English
format Article
sources DOAJ
author Yongqiang Fu
Miaomiao Yang
spellingShingle Yongqiang Fu
Miaomiao Yang
Nonlocal Variational Principles with Variable Growth
Journal of Function Spaces
author_facet Yongqiang Fu
Miaomiao Yang
author_sort Yongqiang Fu
title Nonlocal Variational Principles with Variable Growth
title_short Nonlocal Variational Principles with Variable Growth
title_full Nonlocal Variational Principles with Variable Growth
title_fullStr Nonlocal Variational Principles with Variable Growth
title_full_unstemmed Nonlocal Variational Principles with Variable Growth
title_sort nonlocal variational principles with variable growth
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2014-01-01
description This paper is concerned with the functional J defined by J(u)=∫Ω×ΩW(x,y,∇u(x),∇u(y))dx dy, where Ω⊂ℝN is a regular open bounded set and W is a real-valued function with variable growth. After discussing the theory of Young measures in variable exponent Sobolev spaces, we study the weak lower semicontinuity and relaxation of J.
url http://dx.doi.org/10.1155/2014/435247
work_keys_str_mv AT yongqiangfu nonlocalvariationalprincipleswithvariablegrowth
AT miaomiaoyang nonlocalvariationalprincipleswithvariablegrowth
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