On the asymptotics of the heat equation and bounds on traces associated with the Dirichlet Laplacian

M. van den Berg

Research output: Contribution to journalArticle

Abstract

We use the Feynman-Kac formula and a decomposition of the Brownian bridge to obtain pointwise estimates on the diagonal elements of the heat kernel. We also compute bounds on trace (et?D) where ?D is the Dirichlet Laplacian for (i) a bounded region D in Rn with smooth boundary or (ii) an unbounded region D in R2 with finite area. © 1987.

Original languageEnglish
Pages (from-to)279-293
Number of pages15
JournalJournal of Functional Analysis
Volume71
Issue number2
Publication statusPublished - Apr 1987

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Dirichlet Laplacian
Heat Equation
Trace
Feynman-Kac Formula
Brownian Bridge
Pointwise Estimates
Heat Kernel
Decompose

Cite this

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On the asymptotics of the heat equation and bounds on traces associated with the Dirichlet Laplacian. / van den Berg, M.

In: Journal of Functional Analysis, Vol. 71, No. 2, 04.1987, p. 279-293.

Research output: Contribution to journalArticle

TY - JOUR

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AU - van den Berg, M.

PY - 1987/4

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N2 - We use the Feynman-Kac formula and a decomposition of the Brownian bridge to obtain pointwise estimates on the diagonal elements of the heat kernel. We also compute bounds on trace (et?D) where ?D is the Dirichlet Laplacian for (i) a bounded region D in Rn with smooth boundary or (ii) an unbounded region D in R2 with finite area. © 1987.

AB - We use the Feynman-Kac formula and a decomposition of the Brownian bridge to obtain pointwise estimates on the diagonal elements of the heat kernel. We also compute bounds on trace (et?D) where ?D is the Dirichlet Laplacian for (i) a bounded region D in Rn with smooth boundary or (ii) an unbounded region D in R2 with finite area. © 1987.

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SP - 279

EP - 293

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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