Time-reversal and elliptic boundary value problems
Chen, Zhen-Qing ; Zhang, Tusheng
Ann. Probab., Tome 37 (2009) no. 1, p. 1008-1043 / Harvested from Project Euclid
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In this paper, we prove that there exists a unique, bounded continuous weak solution to the Dirichlet boundary value problem for a general class of second-order elliptic operators with singular coefficients, which does not necessarily have the maximum principle. Our method is probabilistic. The time reversal of symmetric Markov processes and the theory of Dirichlet forms play a crucial role in our approach.
Publié le : 2009-05-15
Classification:  Diffusion,  time-reversal,  Girsanov transform,  Feynman–Kac transform,  multiplicative functional,  partial differential equation,  weak solution,  boundary value problem,  quadratic form,  probabilistic representation,  60J70,  60J57,  35R05,  31C25i,  60H05,  60G46 
@article{1245434027,
     author = {Chen, Zhen-Qing and Zhang, Tusheng},
     title = {Time-reversal and elliptic boundary value problems},
     journal = {Ann. Probab.},
     volume = {37},
     number = {1},
     year = {2009},
     pages = { 1008-1043},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1245434027}
}

Chen, Zhen-Qing; Zhang, Tusheng. Time-reversal and elliptic boundary value problems. Ann. Probab., Tome 37 (2009) no. 1, pp.  1008-1043. http://gdmltest.u-ga.fr/item/1245434027/