Geometric constraints on the domain for a class of minimum problems

Crasta, Graziano; Malusa, Annalisa

doi:10.1051/cocv:2003003

Geodesic

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Geometric constraints on the domain for a class of minimum problems

Crasta, Graziano ; Malusa, Annalisa

ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 125-133

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Résumé

We consider minimization problems of the form $\min_{u \in ϕ + W_{0}^{1, 1} (Ω)} \int_{Ω} [f (D u (x)) - u (x)] d x$ where $Ω \subseteq ℝ^{N}$ is a bounded convex open set, and the Borel function $f : ℝ^{N} \to [0, + \infty]$ 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.

MR Zbl

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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     author = {Crasta, Graziano and Malusa, Annalisa},
     title = {Geometric constraints on the domain for a class of minimum problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {125--133},
     publisher = {EDP-Sciences},
     volume = {9},
     year = {2003},
     doi = {10.1051/cocv:2003003},
     mrnumber = {1957093},
     zbl = {1066.49003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003003/}
}

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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, Tome 9 (2003), pp. 125-133. doi: 10.1051/cocv:2003003

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