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. © 2003 Elsevier Inc. All rights reserved.
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