Zhang, Tusheng; Ran, Qikang Backward SDEs and Sobolev solutions for semilinear parabolic PDEs with singular coefficients. (English) Zbl 1227.60089 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14, No. 3, 517-536 (2011). Summary: We construct the solutions of semilinear parabolic PDEs with singular coefficients and establish the link to solutions of backward stochastic differential equations. Cited in 1 Document MSC: 60H30 Applications of stochastic analysis (to PDEs, etc.) 35K58 Semilinear parabolic equations 35R60 PDEs with randomness, stochastic partial differential equations Keywords:semilinear parabolic partial differential equations; quadratic forms; Dirichlet forms; Sobolev solutions; backward stochastic differential equations PDFBibTeX XMLCite \textit{T. Zhang} and \textit{Q. Ran}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14, No. 3, 517--536 (2011; Zbl 1227.60089) Full Text: DOI References: [1] DOI: 10.1023/A:1007825232513 · Zbl 0982.60057 · doi:10.1023/A:1007825232513 [2] DOI: 10.1007/s00440-007-0065-2 · Zbl 1137.31004 · doi:10.1007/s00440-007-0065-2 [3] DOI: 10.1214/08-AOP427 · Zbl 1187.60064 · doi:10.1214/08-AOP427 [4] DOI: 10.1515/9783110880052.139 · doi:10.1515/9783110880052.139 [5] DOI: 10.1515/9783110889741 · doi:10.1515/9783110889741 [6] Ikeda N., Stochastic Differential Equations and Diffusion Processes (1989) · Zbl 0684.60040 [7] DOI: 10.1080/03605309908821494 · Zbl 0941.35026 · doi:10.1080/03605309908821494 [8] DOI: 10.1016/S0304-4149(01)00124-7 · Zbl 1058.60045 · doi:10.1016/S0304-4149(01)00124-7 [9] DOI: 10.1007/978-3-662-25839-2 · doi:10.1007/978-3-662-25839-2 [10] DOI: 10.1006/jfan.1997.3182 · Zbl 0914.60045 · doi:10.1006/jfan.1997.3182 [11] DOI: 10.1007/978-3-642-77739-4 · doi:10.1007/978-3-642-77739-4 [12] Matoussi A., Elect. J. Probab. 13 pp 1035– · Zbl 1191.35133 · doi:10.1214/EJP.v13-522 [13] DOI: 10.1016/0167-6911(90)90082-6 · Zbl 0692.93064 · doi:10.1016/0167-6911(90)90082-6 [14] Pardoux E., LNCIS 186, in: Stochastic Partial Differential Equations and Their Applications (1992) [15] Peng S., Stoch. Stoch. Rep. 37 pp 61– [16] Prévôt C., Lecture Notes in Mathematics 1905, in: A concise course on stochastic partial differential equations (2007) [17] DOI: 10.1007/BFb0084145 · doi:10.1007/BFb0084145 [18] DOI: 10.1007/978-1-4612-0985-0 · doi:10.1007/978-1-4612-0985-0 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.