Wellposedness of multiple integrals in the calculus of variations. (English) Zbl 0919.49016
Summary: A notion of wellposedness for abstract minimization problems is applied to wellposedness of Dirichlet problems for multiple integrals of the calculus of variations with scalar unknown. Conditions are obtained for the strong convergence of all asymptotically minimizing sequences corresponding to small perturbations of the boundary data. It is also shown that convex problems behave in a simpler way as far as wellposedness is involved.
MSC:
49K40 | Sensitivity, stability, well-posedness |
49J45 | Methods involving semicontinuity and convergence; relaxation |
49K10 | Optimality conditions for free problems in two or more independent variables |