Quantitative unique continuation for the heat equation with Coulomb potentials

Can Zhang

doi:10.3934/mcrf.2018047

Article Contents

2018, Volume 8, Issue 3&4: 1097-1116. Doi: 10.3934/mcrf.2018047

This issue Previous Article Optimal actuator location of the minimum norm controls for stochastic heat equations Next Article

Quantitative unique continuation for the heat equation with Coulomb potentials

Can Zhang^1,2, ,

1.
School of Mathematics and Statistics, Wuhan University, 430072 Wuhan, China
2.
Department of Mathematics, University of the Basque Country (UPV/EHU), 48940 Leioa, Bilbao, Spain

* Corresponding author: Can Zhang
* Corresponding author: Can Zhang

Received: July 2017

Revised: September 2017

Published: September 2018

The author is supported by the National Natural Science Foundation of China under grants 11501424, and by Ministerio de Ciencia e Innovación grant MTM2014-53145-P, Spain

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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 $C^2$-smooth bounded domain. The approach is based on the frequency function method, as well as some parabolic-type Hardy inequalities.

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Mathematics Subject Classification: Primary: 93B07, 93C25.

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