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

We consider minimization problems of the form ${\mathrm{min}}_{u\in \varphi +{W}_{0}^{1,1}\left(\Omega \right)}{\int }_{\Omega }\left[f\left(Du\left(x\right)\right)-u\left(x\right)\right]\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x$ where $\Omega \subseteq {ℝ}^{N}$ is a bounded convex open set, and the Borel function $f:{ℝ}^{N}\to \left[0,+\infty \right]$ is assumed to be neither convex nor coercive. Under suitable assumptions involving the geometry of $\Omega$ 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 : https://doi.org/10.1051/cocv:2003003
Classification:  49J10,  49L25
Keywords: calculus of variations, existence, non-convex problems, non-coercive problems, viscosity solutions
@article{COCV_2003__9__125_0,
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},
publisher = {EDP-Sciences},
volume = {9},
year = {2003},
pages = {125-133},
doi = {10.1051/cocv:2003003},
zbl = {1066.49003},
mrnumber = {1957093},
language = {en},
url = {http://www.numdam.org/item/COCV_2003__9__125_0}
}

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/item/COCV_2003__9__125_0/

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