We prove the lower semicontinuity of a an integral functional of the kind \int_{\Omega}L(x,u(x),Du(x))dx with respect to the convercence induced by L^1_{loc} on W^{1,1}: we suppose that L(x,u,v) has an at least linear growth with respect to v and fulfils a particular property which includes some well-known cases.
A Lower Semicontinuity Theorem for the Integral of the Calculus of Variations / Gavioli, Andrea. - In: ATTI DEL SEMINARIO MATEMATICO E FISICO DELL'UNIVERSITA' DI MODENA. - ISSN 0041-8986. - STAMPA. - 31:(1982), pp. 268-284.
A Lower Semicontinuity Theorem for the Integral of the Calculus of Variations
GAVIOLI, Andrea
1982
Abstract
We prove the lower semicontinuity of a an integral functional of the kind \int_{\Omega}L(x,u(x),Du(x))dx with respect to the convercence induced by L^1_{loc} on W^{1,1}: we suppose that L(x,u,v) has an at least linear growth with respect to v and fulfils a particular property which includes some well-known cases.
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