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Optimal boundary regularity and a Hopf-type lemma for Dirichlet problems involving the logarithmic Laplacian

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arxiv 2401.18033 v2 pith:WQ4MRVJR submitted 2024-01-31 math.AP

Víctor Hernández-Santamaría , Luis Fernando López Ríos , Alberto Saldaña This is my paper · ORCID
classification math.AP
keywords problemssolutionsboundarydirichlethopf-typeinvolvinglaplacianlemma
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Logarithmic Laplacian on General Graphs

    math.AP 2025-07 conditional novelty 6.0 of 10

    The logarithmic Laplacian on weighted graphs is defined via a Bochner integral, given a kernel formula under stochastic completeness, and shown on Z^d to have sharp kernel bounds and exact diffusion asymptotics.

  2. Logarithmic Laplacian on General Riemannian Manifolds

    math.AP 2025-06 conditional novelty 6.0 of 10

    A Bochner integral formula defines the logarithmic Laplacian on complete Riemannian manifolds, with pointwise kernel formulas under Ricci lower bounds and sharp estimates on hyperbolic space.

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