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

On the existence of solutions to a special variational problem

Authors:

Affiliation:

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

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

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, ${|L^prime(|nablatilde w|)|_infty}$ is bounded.

Keywords:

KeywordHeading" >Mathematics Subject Classification (2000) 49K20

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