Non-symmetric stable operators: regularity theory and integration by parts

DOI10.1016/j.aim.2022.108321zbMath1490.45011arXiv2012.04833OpenAlexW3112950629WikidataQ114211535 ScholiaQ114211535MaRDI QIDQ2131768

Joaquim Serra, Xavier Ros-Oton, Enrico Valdinoci, Serena Dipierro

Publication date: 27 April 2022

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.04833

zbMATH Keywords

regularityintegration by partsstable Lévy processesnon-symmetric operators

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Smoothness and regularity of solutions to PDEs (35B65) Integro-partial differential equations (45K05) Stable stochastic processes (60G52) Pseudodifferential operators (47G30) Fractional partial differential equations (35R11) Integro-partial differential equations (35R09)

Related Items (13)

Global Schauder theory for minimizers of the \(H^s(\Omega)\) energy ⋮ Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems ⋮ The principal transmission condition ⋮ Integration by parts for nonsymmetric fractional-order operators on a halfspace ⋮ Harmonic extension technique for non-symmetric operators with completely monotone kernels ⋮ On the regularity theory for mixed local and nonlocal quasilinear elliptic equations ⋮ Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations ⋮ Smooth approximations for fully nonlinear nonlocal elliptic equations ⋮ A generalized fractional Pohozaev identity and applications ⋮ The Dirichlet problem for Lévy-stable operators with \(L^2\)-data ⋮ Weak Harnack inequality for a mixed local and nonlocal parabolic equation ⋮ The fractional obstacle problem with drift: higher regularity of free boundaries ⋮ On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols

Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlocal diffusion and applications
• Regularity theory for general stable operators
• Integration by parts and Pohozaev identities for space-dependent fractional-order operators
• Regularity for parabolic integro-differential equations with very irregular kernels
• Boundary regularity for fully nonlinear integro-differential equations
• Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators
• Intrinsic scaling properties for nonlocal operators
• Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations
• The Evans-Krylov theorem for nonlocal fully nonlinear equations
• Regularity results for nonlocal equations by approximation
• The Pohozaev identity for the fractional Laplacian
• Regularized distance and its applications
• A priori estimates for integro-differential operators with measurable kernels
• Heat kernel estimates for the Dirichlet fractional Laplacian
• Harnack inequalities for jump processes
• Dini and Schauder estimates for nonlocal fully nonlinear parabolic equations with drifts
• The obstacle problem for the fractional Laplacian with critical drift
• On Schauder estimates for a class of nonlocal fully nonlinear parabolic equations
• Dini estimates for nonlocal fully nonlinear elliptic equations
• Polar decomposition of scale-homogeneous measures with application to Lévy measures of strictly stable laws
• Boundary Harnack principle for symmetric stable processes
• Regularity results for nonlocal equations and applications
• The Liouville theorem and linear operators satisfying the maximum principle
• Aleksandrov-Bakelman-Pucci type estimates for integro-differential equations
• Obstacle problems for integro-differential operators: higher regularity of free boundaries
• The weak Harnack inequality for the Boltzmann equation without cut-off
• Local density of solutions to fractional equations
• Definition of fractional Laplacian for functions with polynomial growth
• The Boundary Harnack principle for nonlocal elliptic operators in non-divergence form
• Boundary regularity estimates for nonlocal elliptic equations in \(C^1\) and \(C^{1,\alpha }\) domains
• Estimates and structure of \(\alpha\)-harmonic functions
• Local and nonlocal boundary conditions for \(\mu\)-transmission and fractional elliptic pseudodifferential operators
• Hölder estimates for non-local parabolic equations with critical drift
• Pseudodifferentia Equations on Manifolds with Boundary: Fredholm Property and Asymptotic
• Integro-Differential equations with nonlinear directional dependence
• Regularity theory for parabolic nonlinear integral operators
• Decay rate of harmonic functions for non-symmetric strictly $\alpha $-stable Lévy processes
• Regularity theory for fully nonlinear integro-differential equations
• The boundary Harnack principle for the fractional Laplacian
• Recent Developments in Nonlocal Theory
• Pohozaev identities for anisotropic integrodifferential operators
• Holder estimates for solutions of integro differential equations like the fractional laplace
• C^{1, α}Interior Regularity for Nonlinear Nonlocal Elliptic Equations with Rough Kernels
• Stochastic processes: Theory and methods
• \(C^{\sigma +\alpha}\) regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels

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