کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4589970 1334924 2015 36 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Semi-Dirichlet forms, Feynman–Kac functionals and the Cauchy problem for semilinear parabolic equations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Semi-Dirichlet forms, Feynman–Kac functionals and the Cauchy problem for semilinear parabolic equations
چکیده انگلیسی

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 and regularity of solutions of the problem under mild assumptions on the data.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 268, Issue 5, 1 March 2015, Pages 1205–1240
نویسندگان
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