A $W^1_2$-theory of Stochastic Partial Differential Systems of Divergence type on $C^1$ domains

Details A $W^1_2$-theory of Stochastic Partial Differential Systems of Divergence type on $C^1$ domains A $W^1_2$-theory of Stochastic Partial Differential Systems of Divergence type on $C^1$ domains

2010-07-22

arxiv.org/abs/1007.3830v1

Mathematics

Probability

Scientific paper

In this paper we study the stochastic partial differential systems of divergence type with $C^1$ space domains in $\bR^d$. Existence and uniqueness results are obtained in terms of Sobolev spaces with weights so that we allow the derivatives of the solution to blow up near the boundary. The coefficients of the systems are only measurable and are allowed to blow up near the boundary.

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