Geodesic
On the continuous extension of a generalized solution of the Hamilton-Jacobi equation by characteristics that form a central field of extremals
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 220-235

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The Cauchy problem for the Hamilton-Jacobi equation with state constraints is considered. A justification for a construction of a generalized solution with given structure is provided. The construction is based on the method of characteristics and on solutions of problems related to calculus of variations.
Keywords: Hamilton-Jacobi equations, method of characteristics, viscosity solutions, minimax solutions, extremals.
Mots-clés : calculus of variations 
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     title = {On the continuous extension of a generalized solution of the {Hamilton-Jacobi} equation by characteristics that form a central field of extremals},
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N. N. Subbotina; L. G. Shagalova. On the continuous extension of a generalized solution of the Hamilton-Jacobi equation by characteristics that form a central field of extremals. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 2, pp. 220-235. http://geodesic.mathdoc.fr/item/TIMM_2015_21_2_a18/