Semi-Dirichlet forms, Feynman-Kac functionals and the Cauchy problem for semilinear parabolic equations

被引：13

作者：

Klimsiak, Tomasz ^{[1
]}

机构：

[1] Nicholas Copernicus Univ, Fac Math & Comp Sci, PL-87100 Torun, Poland

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2015年 / 268卷 / 05期

关键词：

Semi-Dirichlet form; Feynman-Kac functional; Semilinear parabolic equation; Measure data; ELLIPTIC-EQUATIONS; HUNT PROCESSES; WEAK SOLUTIONS; BACKWARD SDES; DIVERGENCE; EXISTENCE; SYSTEMS;

D O I：

10.1016/j.jfa.2014.11.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the first part of the paper we prove various results on regularity of Feynman-Kac functionals of Hunt processes associated with time-dependent semi-Dirichlet forms. In the second part we study the Cauchy problem for semilinear parabolic equations with measure data involving operators associated with time-dependent forms. Model examples are non-symmetric divergence form operators and fractional laplacians with possibly variable exponents. We first introduce a definition of a solution resembling Stampacchia's definition in the sense of duality and then, using the results of the first part, we prove the existence, uniqueness an regularity of solutions of the problem under mild assumptions on the data. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：1205 / 1240

页数：36

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