Quantitative uniqueness of continuation result related to Hopf's lemma

2021/05/06 by Mourad Choulli, Choulli, Mourad, Faouzi Triki +3
Computer Science · Mathematics · #35B50 #35C15 #35J08 #35J15 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2105.02588

openalex publication_date 2021/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The classical Hopf's lemma can be reformulated as uniqueness of continuation result. We aim in the present work to quantify this property. We show precisely that if a solution u of a divergence form elliptic equation attains its maximum at a boundary point x₀ then both L¹-norms of u-u(x₀) on the domain and on the boundary are bounded, up to a multiplicative constant, by the exterior normal derivative at x₀.

Citations

• The Green function for uniformly elliptic equations

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