Quantitative unique continuation for the heat equation with Coulomb potentials

2017/07/24 by Can Zhang, Zhang, Can
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1707.07744

openalex publication_date 2017/07/24 · openalex created_date 2017/07/31 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish a Hölder-type quantitative estimate of unique continuation for solutions to the heat equation with Coulomb potentials in either a bounded convex domain or a C²-smooth bounded domain. The approach is based on the frequency function method, as well as some parabolic-type Hardy inequalities.

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