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Time-reversal and elliptic boundary value problems
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.Comment: Published in at http://dx.doi.org/10.1214/08-AOP427 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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