We find a sufficient condition which does not involve global convexity, guaranteeing well-posedness in a strong sense of the minimization of a multiple integral on the Sobolev space W1,1(Ω ℝm) with boundary datum equal to zero. In particular we apply our result to some nonconvex problems recently studied: functionals depending only on the gradient and radially symmetric functionals. © 2005 Society for Industrial and Applied Mathematics.
Well-posedness of nonconvex integral functionals
Villa, Silvia
2005-01-01
Abstract
We find a sufficient condition which does not involve global convexity, guaranteeing well-posedness in a strong sense of the minimization of a multiple integral on the Sobolev space W1,1(Ω ℝm) with boundary datum equal to zero. In particular we apply our result to some nonconvex problems recently studied: functionals depending only on the gradient and radially symmetric functionals. © 2005 Society for Industrial and Applied Mathematics.
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