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

M. van den Berg

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

M. van den Berg

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

32 Citations (Scopus)

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 (e^t?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 language	English
Pages (from-to)	279-293
Number of pages	15
Journal	Journal of Functional Analysis
Volume	71
Issue number	2
Publication status	Published - Apr 1987

Cite this

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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. {\textcopyright} 1987.",

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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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EP - 293

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

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

Abstract

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