Unique Continuation at the Boundary for Harmonic Functions in C1 Domains and Lipschitz Domains with Small Constant

Let Ω⊂ℝn be a C1 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 Ω and continuous in Ω¯, which vanishes in a relatively open subset ∑⊂∂Ω; moreover, the normal derivative ∂νu vanishes in a subset of ∑ wit...

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Bibliographic Details
Published in:Communications on pure and applied mathematics 2023-02, Vol.76 (2), p.305-336
Main Author: Tolsa, Xavier
Format: Article
Language:English
Subjects:
Applications of mathematics
Domains
Harmonic functions
Online Access:Get full text
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Summary:Let Ω⊂ℝn be a C1 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 Ω and continuous in Ω¯, which vanishes in a relatively open subset ∑⊂∂Ω; moreover, the normal derivative ∂νu 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.
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.22025