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Relaxation of bulk and interfacial energies

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Abstract

In this paper we obtain an integral representation for the relaxation inBV(Ω; ℝp) of the functional

$$u \mapsto \int\limits_\Omega {f(x.\nabla u(x))dx + \int\limits_{\sum _{(u)} } {\varphi (x,[u](x),v(x))dH_{N - 1} (x)} }$$

with respect to theBV weak * convergence.

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Authors and Affiliations

  1. Department of Mathematics, Carnegie Mellon University, 15213, Pittsburgh, Pennsylvania

    Ana Cristina Barroso, Guy Bouchitté, Giuseppe Buttazzo & Irene Fonseca

  2. Départment de Mathématiques, Université de Toulon et du Var, BP132, 83957, La Garde Cedex, France

    Ana Cristina Barroso, Guy Bouchitté, Giuseppe Buttazzo & Irene Fonseca

  3. Dipartimento di Matematica, Università di Pisa, Via Buonarroti, 2, 56127, Pisa, Italy

    Ana Cristina Barroso, Guy Bouchitté, Giuseppe Buttazzo & Irene Fonseca

Authors
  1. Ana Cristina Barroso
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  2. Guy Bouchitté
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  3. Giuseppe Buttazzo
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  4. Irene Fonseca
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Communicated byJ. Ball

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Barroso, A.C., Bouchitté, G., Buttazzo, G. et al. Relaxation of bulk and interfacial energies. Arch. Rational Mech. Anal. 135, 107–173 (1996). https://doi.org/10.1007/BF02198453

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