Geometric constraints on the domain for a class of minimum problems
ESAIM: Control, Optimisation and Calculus of Variations, Volume 9 (2003), pp. 125-133.

We consider minimization problems of the form min uϕ+W 0 1,1 (Ω) Ω [f(Du(x))-u(x)]dx 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.

DOI: 10.1051/cocv:2003003
Classification: 49J10, 49L25
Keywords: calculus of variations, existence, non-convex problems, non-coercive problems, viscosity solutions
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     title = {Geometric constraints on the domain for a class of minimum problems},
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Crasta, Graziano; Malusa, Annalisa. Geometric constraints on the domain for a class of minimum problems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 9 (2003), pp. 125-133. doi : 10.1051/cocv:2003003. http://www.numdam.org/articles/10.1051/cocv:2003003/

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