Wellposed convex integral functionals
Danilo Percivale, T. Zolezzi · Numerical Functional Analysis and Optimization · 1997
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 W1 p ω is proved if p >2 and a counterexample is exhibited if p =2.