A new look at the fractional Poisson problem via the logarithmic Laplacian

DOI10.1016/j.jfa.2020.108732zbMath1450.35269arXiv1910.12297OpenAlexW3048652824MaRDI QIDQ2204347

Tobias Weth, Alberto Saldaña, Sven Jarohs

Publication date: 15 October 2020

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.12297

zbMATH Keywords

Green operatorfamily of fractional Poisson problemspointwise monotonicity properties of the solution map

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Fractional partial differential equations (35R11)

Related Items (16)

Small order asymptotics for nonlinear fractional problems ⋮ Fractional Laplacians on ellipsoids ⋮ On fractional higher-order Dirichlet boundary value problems: Between the Laplacian and the bilaplacian ⋮ Small order asymptotics of the Dirichlet eigenvalue problem for the fractional Laplacian ⋮ Small order limit of fractional Dirichlet sublinear-type problems ⋮ Solvability in the sense of sequences for some non-Fredholm operators with the logarithmic Laplacian ⋮ Spectral Properties of the logarithmic Laplacian ⋮ Nonlocal operators of small order ⋮ Solvability in the sense of sequences for some logarithmic Schrödinger operators in higher dimensions ⋮ Bounds for eigenvalues of the Dirichlet problem for the logarithmic Laplacian ⋮ Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods ⋮ Global endpoint regularity estimates for the fractional Dirichlet problem ⋮ On the \(s\)-derivative of weak solutions of the Poisson problem involving the regional fractional Laplacian ⋮ Spectral properties of the logarithmic Laplacian ⋮ Existence and convergence of solutions to fractional pure critical exponent problems ⋮ The logarithmic Schrödinger operator and associated Dirichlet problems

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