New results on Γ-limits of integral functionals

被引:4
|
作者
Ansini, Nadia [1 ]
Dal Maso, Gianni [2 ]
Zeppieri, Caterina Ida [3 ]
机构
[1] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy
[2] SISSA, I-34136 Trieste, Italy
[3] Univ Munster, Inst Numer & Angew Math, D-48149 Munster, Germany
基金
欧洲研究理事会;
关键词
Gamma-convergence; Integral functionals; Localization method; (curl; div)-quasiconvexity; Convergence of minimizers; Convergence of momenta; A-QUASICONVEXITY; CONVERGENCE; OPERATORS;
D O I
10.1016/j.anihpc.2013.02.005
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
For Psi is an element of W-1,W-p (Omega; R-m) and g is an element of W--1,W-p (Omega;R-d), 1 < P < +infinity, we consider a sequence of integral functionals F-k(Psi,g) : W-1,W-p (Omega; R-dxn) -> [0, +infinity] of the form F-k(Psi,g) (u, v) = {integral(Omega) f(k)(x, del u, v) if u - Psi is an element of W-0(1,p) (Omega; R-m) and div upsilon = g, where the integrands f(k) satisfy growth conditions of order p, uniformly in k. We prove a Gamma-compactness result for F-k(Psi,g) with respect to the weak topology of W-1,W-P (Omega; R-m) x L-p (Omega; R-dxn) and we show that under suitable assumptions the integrand of the Gamma-limit is continuously differentiable. We also provide a result concerning the convergence of momenta for minimizers of F-k(Psi,g) (C) 2013 Elsevier Masson SAS. All rights reserved.
引用
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页码:185 / 202
页数:18
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