Minimization of non quasiconvex functionals by integro-extremization method

Sandro Zagatti

doi:10.3934/dcds.2008.21.625

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2008, Volume 21, Issue 2: 625-641. Doi: 10.3934/dcds.2008.21.625

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Minimization of non quasiconvex functionals by integro-extremization method

Sandro Zagatti^1,

1.
S.I.S.S.A. - Via Beirut 2/4 I-34014 Trieste

Received: April 2007

Revised: November 2007

Published: June 2008

Abstract / Introduction Related Papers Cited by

Abstract

We consider non quasiconvex functionals of the form

$\F(u) = \int_\O [f(x,Du(x))+h(x,u(x))]dx$

defined on Sobolev functions subject to Dirichlet boundary conditions. We give an existence result for minimum points, based on regularity assumptions on the minimizers of the relaxed functional, applying the method of extremization of the integral.

Keywords:

Minimum problem,
non quasiconvex functionals.

Mathematics Subject Classification: Primary: 49J45.

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