Partial Differential Equations/Probability Theory
Sobolev weak solutions for parabolic PDEs and FBSDEs

Presented by: Pierre-Louis Lions

Zhang, Feng1
1 School of Mathematics, Shandong University, Jinan, 250100, China
Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 533-536.

This Note is devoted to the representation of Sobolev weak solutions to quasi-linear parabolic PDEs with monotone coefficients via FBSDEs. One distinctive character of this result is that the forward component of the FBSDE is coupled with the backward variable.

Cette Note est consacré à la représentation des solutions faibles au sens de Sobolev d'une EDP quasi-linéaire parabolique avec des coefficients monotones par un système d'EDS et d'EDSR. Un caractère distinctif de ce résultat est que la composante de l'EDS est couplée avec les solutions d'EDSR.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.03.002
Zhang, Feng 1

1 School of Mathematics, Shandong University, Jinan, 250100, China 
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Zhang, Feng. Sobolev weak solutions for parabolic PDEs and FBSDEs. Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 533-536. doi : 10.1016/j.crma.2009.03.002. http://www.numdam.org/articles/10.1016/j.crma.2009.03.002/

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Cited by Sources:

☆ This work was supported by the National Natural Science Foundation (10671112), the National Basic Research Program of China (973 Program, No. 2007CB814904), the Natural Science Foundation of Shandong Province (Z2006A01) and the Doctoral Fund of Education Ministry of China (20060422018).