Quantitative uniqueness of continuation result related to Hopf's lemma

Mourad Choulli (1) , Faouzi Triki (2) , Qi Xue (2)

1 UL - Université de Lorraine
2 EDP - Equations aux Dérivées Partielles

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 $x_0$ then both $L^1$-norms of $u-u(x_0)$ on the domain and on the boundary are bounded, up to a multiplicative constant, by the exterior normal derivative at $x_0$.

Domaines: Equations aux dérivées partielles [math.AP]

Mourad Choulli, Faouzi Triki, Qi Xue. Quantitative uniqueness of continuation result related to Hopf's lemma. 2022. ⟨hal-03606721⟩