Geodesic
On variational approach to the Hamilton-Jacobi PDE
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 4, pp. 613-633.

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In this paper we construct a minimizing sequence for the problem (1). In particular, we show that for any subsolution of the Hamilton-Jacobi equation $(\ast )$ there exists a minimizing sequence weakly convergent to this subsolution. The variational problem (1) arises from the theory of computer vision equations.
Classification : 35E99, 35F20, 49L20, 49L99, 49R50
Keywords: Young measures; computer vision equations 
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     author = {Chabrowski, J. and Zhang, Kewei},
     title = {On variational approach to the {Hamilton-Jacobi} {PDE}},
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Chabrowski, J.; Zhang, Kewei. On variational approach to the Hamilton-Jacobi PDE. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 4, pp. 613-633. http://geodesic.mathdoc.fr/item/CMUC_1993__34_4_a1/