Geometric constraints on the domain for a class of minimum problems
Dip. di Matematica, P.le Aldo Moro 2, 00185 Roma, Italy;
We consider minimization problems of the form where is a bounded convex open set, and the Borel function is assumed to be neither convex nor coercive. Under suitable assumptions involving the geometry of Ω and the zero level set of f, we prove that the viscosity solution of a related Hamilton–Jacobi equation provides a minimizer for the integral functional.
Mathematics Subject Classification: 49J10 / 49L25
Key words: Calculus of Variations / existence / non-convex problems / non-coercive problems / viscosity solutions.
© EDP Sciences, SMAI, 2003