Sobolev weak solutions for parabolic PDEs and FBSDEs

Feng Zhang

doi:10.1016/j.crma.2009.03.002

Partial Differential Equations/Probability Theory

Sobolev weak solutions for parabolic PDEs and FBSDEs
[Solutions faibles de Sobolev des EDP paraboliques et des EDSR]

Présenté par : Pierre-Louis Lions

Feng Zhang ¹

¹ School of Mathematics, Shandong University, Jinan, 250100, China

Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 533-536.

Résumé
Abstract

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.

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.

Reçu le : 2008-11-13
Accepté le : 2009-03-05
Publié le : 2009-03-27

DOI : 10.1016/j.crma.2009.03.002

Affiliations des auteurs :

Feng Zhang ¹

¹ School of Mathematics, Shandong University, Jinan, 250100, China

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     author = {Feng Zhang},
     title = {Sobolev weak solutions for parabolic {PDEs} and {FBSDEs}},
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     pages = {533--536},
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     year = {2009},
     doi = {10.1016/j.crma.2009.03.002},
     language = {en},
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Feng Zhang. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.03.002/

Bibliographie
Cité par

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Cité par 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).

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