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 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.
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}, pages = {125--133}, publisher = {EDP-Sciences}, volume = {9}, year = {2003}, doi = {10.1051/cocv:2003003}, mrnumber = {1957093}, zbl = {1066.49003}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2003003/} }
TY - JOUR AU - Crasta, Graziano AU - Malusa, Annalisa TI - Geometric constraints on the domain for a class of minimum problems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2003 SP - 125 EP - 133 VL - 9 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2003003/ DO - 10.1051/cocv:2003003 LA - en ID - COCV_2003__9__125_0 ER -
%0 Journal Article %A Crasta, Graziano %A Malusa, Annalisa %T Geometric constraints on the domain for a class of minimum problems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2003 %P 125-133 %V 9 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2003003/ %R 10.1051/cocv:2003003 %G en %F 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/articles/10.1051/cocv:2003003/
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