Strong unique continuation for variable coefficient parabolic operators with Hardy type potential

2022/06/27 by Banerjee, Agnid, Ganguly, Pritam, Ghosh, Abhishek
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.13328

Abstract

In this paper, we prove the strong unique continuation property at the origin for solutions of the following scaling critical parabolic differential inequality |div (A(x,t) ∇ u) - u_t| ≤ \fracM|x|² |u|, where the coefficient matrix A is Lipschitz continuous in x and t. Our main result sharpens a previous one of Vessella concerned with the subcritical case as well as extends a recent result of one of us with Garofalo and Manna for the heat operator.

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