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.
@article{118620, author = {Jan H. Chabrowski and Ke Wei Zhang}, title = {On variational approach to the Hamilton-Jacobi PDE}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {34}, year = {1993}, pages = {613-633}, zbl = {0802.49021}, mrnumber = {1263792}, language = {en}, url = {http://dml.mathdoc.fr/item/118620} }
Chabrowski, Jan H.; Zhang, Ke Wei. On variational approach to the Hamilton-Jacobi PDE. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 613-633. http://gdmltest.u-ga.fr/item/118620/
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