A W¹₂-theory of Stochastic Partial Differential Systems of Divergence type on C¹ domains

2010/07/22 by Kyeong-Hun Kim, Kim, Kyeong-Hun, Kijung Lee +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.1007.3830

arxiv created 2010/07/22 · openalex publication_date 2010/07/22 · arxiv updated 2010/07/23 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper we study the stochastic partial differential systems of divergence type with C¹ 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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