Unique Continuation at the Boundary for Harmonic Functions in C1 Domains and Lipschitz Domains with Small Constant
Xavier Tolsa · Communications on Pure and Applied Mathematics · 2021
Abstract Let be a domain, or more generally, a Lipschitz domain with small local Lipschitz constant. In this paper it is shown that if u is a function harmonic in and continuous in , which vanishes in a relatively open subset ; moreover, the normal derivative vanishes in a subset of with positive surface measure; then u is identically zero. © 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.