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Article type: Research Article
Authors: Serafin, G.; *
Affiliations: Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Poland. E-mail: [email protected]
Correspondence: [*] Corresponding author. E-mail: [email protected].
Abstract: We establish short-time asymptotics with rates of convergence for the Laplace Dirichlet heat kernel in a ball. So far, such results were only known in simple cases where explicit formulae are available, i.e., for sets as half-line, interval and their products. Presented asymptotics may be considered as a complement or a generalization of the famous “principle of not feeling the boundary” in case of a ball. Following the metaphor, the principle reveals when the process does not feel the boundary, while we describe what happens when it starts feeling the boundary.
Keywords: Heat kernel, ball, asymptotics, Laplacian, Brownian motion
DOI: 10.3233/ASY-211734
Journal: Asymptotic Analysis, vol. 129, no. 3-4, pp. 379-412, 2022
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