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Geometric constraints on the domain for a class of minimum problems

Graziano CrastaAnnalisa Malusa — 2003

ESAIM: Control, Optimisation and Calculus of Variations

We consider minimization problems of the form min u ϕ + W 0 1 , 1 ( Ω ) Ω [ f ( D u ( x ) ) - u ( x ) ] d x where Ω N is a bounded convex open set, and the Borel function f : N [ 0 , + ] 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.

Geometric constraints on the domain for a class of minimum problems

Graziano CrastaAnnalisa Malusa — 2010

ESAIM: Control, Optimisation and Calculus of Variations

We consider minimization problems of the form min u ϕ + W 0 1 , 1 ( Ω ) Ω [ f ( D u ( x ) ) - u ( x ) ] d x where Ω N is a bounded convex open set, and the Borel function f : N [ 0 , + ] is assumed to be neither convex nor coercive. Under suitable assumptions involving the geometry of and the zero level set of , we prove that the viscosity solution of a related Hamilton–Jacobi equation provides a minimizer for the integral functional.

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