American Institute of Mathematical Sciences

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June  2008, 21(2): 625-641. doi: 10.3934/dcds.2008.21.625

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, Italy

Received  April 2007 Revised  November 2007 Published  March 2008

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: non quasiconvex functionals., Minimum problem.
Mathematics Subject Classification: Primary: 49J4.
Citation: Sandro Zagatti. Minimization of non quasiconvex functionals by integro-extremization method. Discrete & Continuous Dynamical Systems, 2008, 21 (2) : 625-641. doi: 10.3934/dcds.2008.21.625
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