Two-sided estimates on Dirichlet heat kernels for time-dependent parabolic operators with singular drifts in C1,α-domains

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Cho, Sungwon²  Kim, Panki^3,4  Park, Hyein¹ 

[1] Korea Adv Inst Sci & Technol, Dept Math Sci, Taejon 305701, South Korea

[2] Gwangju Natl Univ Educ, Dept Math Educ, Kwangju 500703, South Korea

[3] Seoul Natl Univ, Dept Math, Seoul 151747, South Korea

[4] Seoul Natl Univ, Res Inst Math, Seoul 151747, South Korea

关键词: Heat kernel estimates;    Dirichlet heat kernel;    Time-dependent operator;    Parabolic operator;    Singular measure drift;    Parabolic Kato class;    Dini continuous;    Green function estimate;   

DOI  :  10.1016/j.jde.2011.07.025

来源: Elsevier

【 摘 要 】

In this paper, we establish sharp two-sided estimates for the Dirichlet heat kernels of a large class of time-dependent parabolic operators with singular drifts in C-1,C-alpha-domain in R-d, where d >= 1 and alpha is an element of (0,1]. Our operator is L + mu . del(x), where L is a time-dependent uniformly elliptic divergent operator with Dini continuous coefficients and mu is a signed measure on (0, infinity) x R-d belonging to parabolic Kato class. Along the way, a gradient estimate is also established. Our method employs a combination of partial differential equations and perturbation techniques. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free