Open AccessMinimization of non quasiconvex functionals by integro-extremization method
Author(s) -
Sandro Zagatti
Publication year - 2008
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2008.21.625
Subject(s) - quasiconvex function , mathematics , sobolev space , mathematical analysis , boundary (topology) , pure mathematics , dirichlet distribution , dirichlet boundary condition , boundary value problem , regular polygon , subderivative , geometry , convex optimization
We consider non quasiconvex functionals of the form\ud\begin{displaymath}\ud\F(u) = \int_\O [f(x,Du(x))+h(x,u(x))]dx\ud\end{displaymath}\uddefined on Sobolev functions subject to Dirichlet boundary conditions. \udWe give an existence result for minimum points, based on regularity assumptions on\udthe minimizers of the relaxed functional, applying the method of extremization \udof the integral