Optimal boundary regularity and a Hopf-type lemma for Dirichlet problems involving the logarithmic Laplacian
Analysis of PDEs
2024-07-08 v2
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.
Keywords
Cite
@article{arxiv.2401.18033,
title = {Optimal boundary regularity and a Hopf-type lemma for Dirichlet problems involving the logarithmic Laplacian},
author = {Víctor Hernández-Santamaría and Luis Fernando López Ríos and Alberto Saldaña},
journal= {arXiv preprint arXiv:2401.18033},
year = {2024}
}
Comments
Revised version, 30 pages