Archivio Istituzionale della RicercaWe prove some existence and regularity results for minimizers of a class of integral functionals, defined on vector-valued Sobolev functions u for which the volumes of certain level-sets {u=l_i} are prescribed, with i=1,...,m. More specifically, in the case of the energy density |D u|^2 + F(u), we prove that minimizers exist and are locally Lipschitz, if the function F and {l_1,...,l_m} verify suitable hypotheses.
On a constrained variational problem in the vector-valued case / Leonardi, G; Tilli, Paolo. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 85:(2006), pp. 251-268.
On a constrained variational problem in the vector-valued case
TILLI, PAOLO
2006
Abstract
We prove some existence and regularity results for minimizers of a class of integral functionals, defined on vector-valued Sobolev functions u for which the volumes of certain level-sets {u=l_i} are prescribed, with i=1,...,m. More specifically, in the case of the energy density |D u|^2 + F(u), we prove that minimizers exist and are locally Lipschitz, if the function F and {l_1,...,l_m} verify suitable hypotheses.
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https://hdl.handle.net/11583/1406454
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