Geometric constraints on the domain for a class of minimum problems
Graziano Crasta, Annalisa Malusa · ESAIM Control Optimisation and Calculus of Variations · 2003
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.