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- Title
Optimal boundary regularity and a Hopf-type lemma for Dirichlet problems involving the logarithmic Laplacian.
- Authors
Hernández-Santamaría, Víctor; Ríos, Luis Fernando López; Saldaña, Alberto
- Abstract
We study the optimal boundary regularity of solutions to Dirichlet problems involving the logarithmic Laplacian. Our proofs are based on the construction of suitable barriers via the Kelvin transform and direct computations. As applications of our results, we show a Hopf-type lemma for nonnegative weak solutions and the uniqueness of solutions to some nonlinear problems.
- Subjects
DIRICHLET problem; NONLINEAR equations
- Publication
Discrete & Continuous Dynamical Systems: Series A, 2025, Vol 45, Issue 1, p1
- ISSN
1078-0947
- Publication type
Article
- DOI
10.3934/dcds.2024084