Work

Removability of the fundamental singularity for the heat equation and its consequences

Year: 2024

Type: article

Abstract: We prove the necessary and sufficient condition for the removability of the fundamental singularity, and equivalently for the unique solvability of the singular Dirichlet problem for the heat equation. In the measure-theoretical context the criterion determines whether the h-parabolic measure of the singularity point is null or positive. From the probabilistic point of view, the criterion presents an asymptotic law for conditional Brownian motion.

Source: Journal of Mathematical Physics

DOI: 10.1063/5.0233490

Author: Ugur G. Abdulla

Institution: Okinawa Institute of Science and Technology Graduate University

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W4405358622

FWCI:

Cites: 21

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Related to: 10