We study the Dirichlet problem for degenerate elliptic equations, and show that the probabilistic solution is a unique viscosity solution.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba54-2-8, author = {Chuandi Liu and Hiroaki Morimoto}, title = {The Probabilistic Solution of the Dirichlet Problem for Degenerate Elliptic Equations}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {54}, year = {2006}, pages = {163-174}, zbl = {1105.60059}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba54-2-8} }
Chuandi Liu; Hiroaki Morimoto. The Probabilistic Solution of the Dirichlet Problem for Degenerate Elliptic Equations. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 54 (2006) pp. 163-174. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba54-2-8/