Communications in Mathematical Analysis

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

Lotfi Riahi

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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

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

First available in Project Euclid: 18 July 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 31B25, 35K05, 47D06

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


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.

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