On the existence of solutions to a special variational problem期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On the existence of solutions to a special variational problem

Authors:

Institution:

1.Dipartimento di Matematica e Applicazioni,Università degli Studi di Milano-Bicocca,Milan,Italy;2.Departamento de Matemática,Universidade de évora,évora,Portugal

Abstract:

In this paper we establish an existence and regularity result for solutions to the problem

$\mbox{minimize}\int\limits_{\Omega} L(|\nabla u(x)|)\,dx \quad {\rm on }\{u: u-u _0 \in W^{1,1}_0(\Omega)\}$

for boundary data that are constant on each connected component of the boundary of Ω. The Lagrangean L belongs to a class that contains both extended valued Lagrangeans and Lagrangeans with linear growth. Regularity means that the solution ${\tilde w}$ is Lipschitz continuous and that, in addition, ${\|L^\prime(|\nabla\tilde w|)\|_\infty}$ is bounded.

Keywords:

Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 49K20

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