Quasiconvexification of geometric integrals期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Quasiconvexification of geometric integrals

Authors:

Email author" target="_blank">Jean-Philippe?Mandallena Email author

Institution:

1.EMIAN (Equipe de Mathématiques, Informatique et Applications de N?mes),Centre Universitaire de Formation et de Recherche de N?mes,N?mes,France;2.I3M (Institut de Mathématiques et Modélisation de Montpellier) UMR, CNRS 5149,Université Montpellier II,Montpellier,France

Abstract:

We study the existence of an integral representation for the functional

$L^p_\mu(\Omega;\mathbb{R}^m)\ni{u}\mapsto\inf\left\{\liminf_{n\to+\infty}\int_\Omega{f}(\nabla{u}_n(x))d\mu(x):C^\infty(\overline{\Omega};\mathbb{R}^m)\ni{u}_n\stackrel{L^p_\mu}{\to} u\right\},$

when μ is a positive Radon measure on ℝ^N, Ω⊂ℝ^N is a bounded open set, and $f:\mathbb{M}^{m\times{N}}\to0,+\infty$ is a continuous function not necessarily convex with growth conditions of order p>1. Mathematics Subject Classification (2000) 49J45, 49Q20

Keywords:

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