We study connections between Sobolev space solutions of the Dirichlet problem for semilinear second order elliptic equations in divergence form and solutions of backward stochastic differential equations with random terminal time.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-1-1, author = {Andrzej Rozkosz}, title = {BSDEs with random terminal time and semilinear elliptic PDEs in divergence form}, journal = {Studia Mathematica}, volume = {166}, year = {2005}, pages = {1-21}, zbl = {1067.60056}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-1-1} }
Andrzej Rozkosz. BSDEs with random terminal time and semilinear elliptic PDEs in divergence form. Studia Mathematica, Tome 166 (2005) pp. 1-21. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-1-1/