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Article Dans Une Revue Journal de Mathématiques Pures et Appliquées Année : 2000

On the relaxation of nonconvex superficial integral functionals

Résumé

We present a new approach to the variational relaxation of functionals $F:D(\mathbb{R}^N;\mathbb{R}^m)\to[0,\infty[$ of the type: $$ F(v):=\int_{\mathbb{R}^N}W(\nabla v(x))d\mu(x), $$ where $W:\mathbb{R}^{mN}\to[0,\infty[$ is a continuous function with growth conditions of order $p\geq 1$ but not necessarily convex. We essentially study the case when $\mu$ is the $k$-dimensional Hausdorff measure restricted to a suitable piece of a $k$-dimensional smooth submanifold of $\mathbb{R}^N$.

Dates et versions

hal-01644831 , version 1 (22-11-2017)

Identifiants

Citer

Jean-Philippe Mandallena. On the relaxation of nonconvex superficial integral functionals. Journal de Mathématiques Pures et Appliquées, 2000, 79 (10), pp.1011 - 1028. ⟨10.1016/S0021-7824(00)01184-3⟩. ⟨hal-01644831⟩
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