A+ CATEGORY SCIENTIFIC UNIT

Lower semicontinuous envelopes in $W^{1,1}\times L^{p}$

Volume 101 / 2014

Ana Margarida Ribeiro, Elvira Zappale Banach Center Publications 101 (2014), 187-206 MSC: 49J45; 74F99. DOI: 10.4064/bc101-0-15

Abstract

The lower semicontinuity of functionals of the type ${\int_\Omega f(x,u,v,\nabla u)\, dx }$ with respect to the $(W^{1,1}\times L^p)$-weak$^\ast$ topology is studied. Moreover, in absence of lower semicontinuity, an integral representation in $W^{1,1}\times L^p$ for the lower semicontinuous envelope is also provided.

Authors

  • Ana Margarida RibeiroCentro de Matemática e Aplicações (CMA)
    Departamento de Matemática
    Faculdade de Ciências e Tecnologia
    Universidade Nova de Lisboa
    Quinta da Torre
    2829-516 Caparica, Portugal
    e-mail
  • Elvira ZappaleDipartimento di Ingegneria Industriale
    Università degli Studi di Salerno
    via Giovanni Paolo II 132
    84084, Fisciano (SA), Italy
    e-mail

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