Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Minimization of non quasiconvex functionals by integro-extremization method

Pages: 625 - 641, Volume 21, Issue 2, June 2008      doi:10.3934/dcds.2008.21.625

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Sandro Zagatti - S.I.S.S.A. - Via Beirut 2/4 I-34014 Trieste, Italy (email)

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.

Received: April 2007;      Revised: November 2007;      Available Online: March 2008.