Exact Green's formula for the fractional Laplacian and perturbations

DOI10.7146/math.scand.a-120889zbMath1453.35051arXiv1904.03648OpenAlexW2926312600MaRDI QIDQ5135283

Gerd Grubb

Publication date: 19 November 2020

Published in: MATHEMATICA SCANDINAVICA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.03648

zbMATH Keywords

Green formulapseudo-differential operatorfractional Laplacian

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fractional partial differential equations (35R11) Green's functions for elliptic equations (35J08)

Related Items (5)

Well-posedness for a class of pseudodifferential diffusion equations on the torus ⋮ On the Landis conjecture for the fractional Schrödinger equation ⋮ Higher-order fractional Laplacians: An overview ⋮ Drift diffusion equations with fractional diffusion on compact Lie groups ⋮ A non-local inverse problem with boundary response

Cites Work

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• Large \(s\)-harmonic functions and boundary blow-up solutions for the fractional Laplacian
• Integration by parts and Pohozaev identities for space-dependent fractional-order operators
• Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators
• Local integration by parts and Pohozaev identities for higher order fractional Laplacians
• The Pohozaev identity for the fractional Laplacian
• Boundary integral equations
• Positive powers of the Laplacian in the half-space under Dirichlet boundary conditions
• Functional calculus of pseudodifferential boundary problems.
• Fractional-order operators: boundary problems, heat equations
• Limited regularity of solutions to fractional heat and Schrödinger equations
• Local and nonlocal boundary conditions for \(\mu\)-transmission and fractional elliptic pseudodifferential operators
• Regularity of spectral fractional Dirichlet and Neumann problems
• Pseudo-differential boundary problems in L_p, spaces
• Distributions and Operators
• Integral representation of solutions to higher-order fractional Dirichlet problems on balls
• Pohozaev identities for anisotropic integrodifferential operators
• Green’s formula and a Dirichlet-to-Neumann operator for fractional-order pseudodifferential operators
• Differential operators and boundary value problems on hypersurfaces

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