Sufficient conditions are obtained for wellposedness of convex minimum problems of the calculus of variations for multiple integrals under strong or weak perturbations of the boundary data. Problems with a unique minimizer as well as problems with several solutions are treated. Wellposedness under weak convergence of the boundary data in W-1,W-p(Omega) is proved if p > 2, and a counterexample is exhibited if p = 2.
Wellposed convex integral functionals
PERCIVALE, DANILO;
1997-01-01
Abstract
Sufficient conditions are obtained for wellposedness of convex minimum problems of the calculus of variations for multiple integrals under strong or weak perturbations of the boundary data. Problems with a unique minimizer as well as problems with several solutions are treated. Wellposedness under weak convergence of the boundary data in W-1,W-p(Omega) is proved if p > 2, and a counterexample is exhibited if p = 2.
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