A chain rule in the space L^1(div;A) is obtained under weak regularity conditions. This chain rule has important applications in the study of lower semicontinuity problems for functionals of the form \int_A (a(x,u)+b(x,u)Du)dx, in W1,1(A) with respect to strong convergence in L^1(A) and in turn for general functionals of the form F(u,A):=\int_A f(x,u(x),Du(x))dx, in W^{1,1}(A). Classical results of Serrin and of De Giorgi, Buttazzo and Dal Maso are extended and generalized.

A chain rule in L^1(div;Omega) and its applications to lower semicontinuity / DE CICCO, Virginia; G., Leoni. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 19:(2004), pp. 23-51. [10.1007/s00526-003-0192-2]

A chain rule in L^1(div;Omega) and its applications to lower semicontinuity

DE CICCO, Virginia;
2004

Abstract

A chain rule in the space L^1(div;A) is obtained under weak regularity conditions. This chain rule has important applications in the study of lower semicontinuity problems for functionals of the form \int_A (a(x,u)+b(x,u)Du)dx, in W1,1(A) with respect to strong convergence in L^1(A) and in turn for general functionals of the form F(u,A):=\int_A f(x,u(x),Du(x))dx, in W^{1,1}(A). Classical results of Serrin and of De Giorgi, Buttazzo and Dal Maso are extended and generalized.
2004
CHAIN RULE; LOWER SEMICONTINUITY; vectorial fields with integrable divergence
01 Pubblicazione su rivista::01a Articolo in rivista
A chain rule in L^1(div;Omega) and its applications to lower semicontinuity / DE CICCO, Virginia; G., Leoni. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 19:(2004), pp. 23-51. [10.1007/s00526-003-0192-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/71560
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