Quantitative unique continuation for the stochastic heat equation with singular potentials
Abstract
Abstract In this paper, we present a Hölder‐type quantitative assessment of unique continuation properties concerning solutions to the stochastic heat equation featuring singular potentials. We explore this phenomenon within the confines of both bounded convex domains and ‐smooth bounded domains. Our methodology draws inspiration from the frequency function method and incorporates parabolic‐type Hardy inequalities in stochastic case. Notably, these investigations, to the best of our knowledge, represent pioneering endeavors within the context of this equation.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Differential Equations and Boundary Problems
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
- Volume
- 106
- Issue
- 2
- Publication date
- 1 February 2026
- Language
- EN