Communications in Mathematical Analysis

Estimates for Dirichlet Heat Kernels, Intrinsic Ultracontractivity and Expected Exit Time on Lipschitz Domains

Lotfi Riahi

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Abstract

We prove pointwise estimates for the heat kernel of a secondorder elliptic operator with Dirichlet boundary conditions on a bounded Lipschitz domain in $\mathbb{R}^n,\, n\geq 1$. Applications to obtain estimates for intrinsic ultracontractivity of the heat semigroup and expected exit time of a Brownian motion are given.

Article information

Source
Commun. Math. Anal., Volume 15, Number 1 (2013), 115-130.

Dates
First available in Project Euclid: 18 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.cma/1374153498

Mathematical Reviews number (MathSciNet)
MR3082267

Zentralblatt MATH identifier
1277.31014

Subjects
Primary: 31B25, 35K05, 47D06

Keywords
Boundary behavior heat kernel Dirichlet boundary conditions elliptic operator Green function Lipschitz domain intrinsic ultracontractivity exit time

Citation

Riahi , Lotfi. Estimates for Dirichlet Heat Kernels, Intrinsic Ultracontractivity and Expected Exit Time on Lipschitz Domains. Commun. Math. Anal. 15 (2013), no. 1, 115--130. https://projecteuclid.org/euclid.cma/1374153498


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