Publication 98-CNA-10

Lower semicontinuity and relaxation

and

G. Leoni
Dipartimento di Scienze e Tecnologie Avanzate
Universita del Piemonte Orientale
Alessandria, Italy 15100

ABSTRACT: Lower semicontinuity and relaxation results in BV are obtained for multiple integrals $$ F(u,\Omega):=\int_\Omega f(x,u(x),\nabla u(x))\,dx, \quad u \in W^{1,1}(\Omega;\Bbb R^d), $$ where the energy density f satisfies lower semicontinuity conditions with respect to (x,u) and is not subjected to coercivity hypotheses. These results call for methods recently developed in the Calculus of Variations.

 

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• 98-CNA-010.dvi
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