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A chain rule in \(L^{1}\left({\operatorname*{div};\Omega}\right)\) and its applications to lower semicontinuity

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Abstract.

A chain rule in the space \(L^{1}\left(\operatorname*{div};\Omega\right) \) is obtained under weak regularity conditions. This chain rule has important applications in the study of lower semicontinuity problems for general functionals of the form \(\int_{\Omega}f(x,u,\nabla u) dx\) with respect to strong convergence in \(L^{1}\left(\Omega\right) \) . Classical results of Serrin and of De Giorgi, Buttazzo and Dal Maso are extended and generalized.

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Authors and Affiliations

  1. Dipartimento di Metodi e Modelli, Matematici per le Scienze Applicate, Universitá di Roma “La Sapienza”, Via Scarpa 16, I-00161, Rome, Italy

    Virginia De Cicco & Giovanni Leoni

Authors
  1. Virginia De Cicco
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  2. Giovanni Leoni
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Received: 1 June 2002, Accepted: 7 January 2003, Published online: 6 June 2003

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Cicco, V.D., Leoni, G. A chain rule in \(L^{1}\left({\operatorname*{div};\Omega}\right)\) and its applications to lower semicontinuity. Cal Var 19, 23–51 (2003). https://doi.org/10.1007/s00526-003-0192-2

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  • DOI: https://doi.org/10.1007/s00526-003-0192-2

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