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

Krzysztof Burdzy*, Zhen Qing Chen, John Sylvester

*此作品的通讯作者

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18 引用 （Scopus）
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摘要

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.

源语言英语
页（从-至）1-34
页数34
期刊Journal of Functional Analysis
卷204
期1
DOI
出版状态已出版 - 20 10月 2003
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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