We prove some existence and regularity results for minimizers of a class of integralfunctionals, defined on vector-valued Sobolev functions u for which the volumes ofcertain level-sets {u = li} are prescribed, with i = 1, . . . ,m. More specifically, in thecase of the energy density W(x, u,Du) = |Du|2+F(u), we prove that minimizers existand are locally Lipschitz, if the function F and {l1, . . . , lm} verify suitable hypotheses.
On a constrained variational problem in the vector-valued case / Leonardi, Gian Paolo; Tilli, P.. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 85:2(2006), pp. 251-268. [10.1016/j.matpur.2005.07.004]
On a constrained variational problem in the vector-valued case
LEONARDI, Gian Paolo;
2006
Abstract
We prove some existence and regularity results for minimizers of a class of integralfunctionals, defined on vector-valued Sobolev functions u for which the volumes ofcertain level-sets {u = li} are prescribed, with i = 1, . . . ,m. More specifically, in thecase of the energy density W(x, u,Du) = |Du|2+F(u), we prove that minimizers existand are locally Lipschitz, if the function F and {l1, . . . , lm} verify suitable hypotheses.
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