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Weak Solutions of Semilinear PDEs in Sobolev Spaces and Their Probabilistic Interpretation via the FBSDEs |
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| Authors: | Youssef Ouknine |
| Institution: | Department of Mathematics , Faculty of Sciences Semlalia , Marrakech, Morocco |
| Abstract: | Abstract The article is devoted to representation of weak solutions (in Sobolev sense) of degenerate parabolic partial differential equations through forward-backward stochastic differential equations. Before, we prove a weak version of a norm equivalence result. |
| Keywords: | Forward backward stochastic differential equation Semilinear partial differential equation Weighted Sobolev spaces |