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A-Quasiconvexity: Relaxation and Homogenization

  • Andrea Braides (a1), Irene Fonseca (a2) and Giovanni Leoni (a3)

Abstract

Integral representation of relaxed energies and of Γ-limits of functionals $$ (u,v)\mapsto \int_\Omega f( x,u(x),v(x))\,dx $$ are obtained when sequences of fields v may develop oscillations and are constrained to satisfy a system of first order linear partial differential equations. This framework includes the treatement of divergence-free fields, Maxwell's equations in micromagnetics, and curl-free fields. In the latter case classical relaxation theorems in W1,p , are recovered.

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A-Quasiconvexity: Relaxation and Homogenization

  • Andrea Braides (a1), Irene Fonseca (a2) and Giovanni Leoni (a3)

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