The heat equation and reflected Brownian motion in time-dependent domains. II. Singularities of solutions

Krzysztof Burdzy; Zhen Qing Chen; John Sylvester

doi:10.1016/S0022-1236(03)00128-9

The heat equation and reflected Brownian motion in time-dependent domains. II. Singularities of solutions

Krzysztof Burdzy^*, Zhen Qing Chen, John Sylvester

^*Corresponding author for this work

University of Washington

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

18 Citations (Scopus)

Abstract

We study the space-time Brownian motion and the heat equation in non-cylindrical domains. The paper is mostly devoted to singularities of the heat equation near rough points of the boundary. Two types of singularities are identified - heat atoms and heat singularities. A number of explicit geometric conditions are given for the existence of singularities. Other properties of the heat equation solutions are analyzed as well.

Original language	English
Pages (from-to)	1-34
Number of pages	34
Journal	Journal of Functional Analysis
Volume	204
Issue number	1
DOIs	https://doi.org/10.1016/S0022-1236(03)00128-9
Publication status	Published - 20 Oct 2003
Externally published	Yes

Keywords

Brownian motion
Heat equation
Neumann boundary conditions
Non-cylindrical domains
Parabolic equations
Space-time Brownian motion

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10.1016/S0022-1236(03)00128-9

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Burdzy, K., Chen, Z. Q., & Sylvester, J. (2003). The heat equation and reflected Brownian motion in time-dependent domains. II. Singularities of solutions. Journal of Functional Analysis, 204(1), 1-34. https://doi.org/10.1016/S0022-1236(03)00128-9

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abstract = "We study the space-time Brownian motion and the heat equation in non-cylindrical domains. The paper is mostly devoted to singularities of the heat equation near rough points of the boundary. Two types of singularities are identified - heat atoms and heat singularities. A number of explicit geometric conditions are given for the existence of singularities. Other properties of the heat equation solutions are analyzed as well.",

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AU - Chen, Zhen Qing

AU - Sylvester, John

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Y1 - 2003/10/20

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AB - We study the space-time Brownian motion and the heat equation in non-cylindrical domains. The paper is mostly devoted to singularities of the heat equation near rough points of the boundary. Two types of singularities are identified - heat atoms and heat singularities. A number of explicit geometric conditions are given for the existence of singularities. Other properties of the heat equation solutions are analyzed as well.

KW - Brownian motion

KW - Heat equation

KW - Neumann boundary conditions

KW - Non-cylindrical domains

KW - Parabolic equations

KW - Space-time Brownian motion

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ER -

The heat equation and reflected Brownian motion in time-dependent domains. II. Singularities of solutions

Abstract

Keywords

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