-convergence of equi-coercive nonlinear energies defined on vector-valued functions, with non-uniformly bounded coefficients

详细信息    查看全文

• 作者：M. Briane^a ; ^{mbriane@insa-rennes.fr} ; J. Casado-Dí ; az^b ; ^{jcasadod@us.es} ; M. Luna-Laynez^b ; ^{mllaynez@us.es} ; A. Pallares-Martí ; n^b ; ^{ajpallares@us.es}
• 关键词：35B27 ; 74B20
• 刊名：Nonlinear Analysis: Theory, Methods & Applications
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：151
• 期：Complete
• 页码：187-207
• 全文大小：797 K
• 卷排序：151

文摘

The present paper deals with the asymptotic behavior of equi-coercive sequences {ℱ_{n}{ℱn} of nonlinear functionals defined over vector-valued functions in W01,p(Ω)M, where p>1p>1, M≥1M≥1, and ΩΩ is a bounded open set of RNRN, N≥2N≥2. The strongly local energy density Fn(⋅,Du)Fn(⋅,Du) of the functional ℱnℱn satisfies a Lipschitz condition with respect to the second variable, which is controlled by a positive sequence {an}{an} which is only bounded in some suitable space Lr(Ω)Lr(Ω). We prove that the sequence {ℱn}{ℱn}ΓΓ-converges for the strong topology of Lp(Ω)MLp(Ω)M to a functional ℱℱ which has a strongly local density F(⋅,Du)F(⋅,Du) for sufficiently regular functions uu. This compactness result extends former results on the topic, which are based either on maximum principle arguments in the nonlinear scalar case, or adapted div–curl lemmas in the linear case. Here, the vectorial character and the nonlinearity of the problem need a new approach based on a careful analysis of the asymptotic minimizers associated with the functional ℱnℱn. The relevance of the conditions which are imposed to the energy density Fn(⋅,Du)Fn(⋅,Du), is illustrated by several examples including some classical hyperelastic energies.}