Regularity theory for general stable operators

DOI10.1016/j.jde.2016.02.033zbMath1346.35220arXiv1412.3892OpenAlexW2963729625MaRDI QIDQ266400

Xavier Ros-Oton, Joaquim Serra

Publication date: 13 April 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.3892

zbMATH Keywords

interior regularityboundary regularitystable Lévy processes

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Stable stochastic processes (60G52) Pseudodifferential operators (47G30) Fractional partial differential equations (35R11)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Liouville theorems for a general class of nonlocal operators
• Regularity for parabolic integro-differential equations with very irregular kernels
• Boundary regularity for fully nonlinear integro-differential equations
• Non-local gradient dependent operators
• Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators
• Regularity for fully nonlinear nonlocal parabolic equations with rough kernels
• Approximation of multidimensional stable densities
• Regularity of harmonic functions for a class of singular stable-like processes
• Regularity results for stable-like operators
• Asymptotic behaviour of densities of stable semigroups of measures
• A global calculus of parameter-dependent pseudodifferential boundary problems in \(L_ p\) Sobolev spaces
• Estimating the spectral measure of a multivariate stable distribution via spherical harmonic analysis.
• Harnack inequalities for jump processes
• Harnack's inequality for stable Lévy processes
• Analysis of jump processes with nondegenerate jumping kernels
• The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
• Local and nonlocal boundary conditions for \(\mu\)-transmission and fractional elliptic pseudodifferential operators
• On multipliers of Fourier integrals in the spaces \(L_{p,\theta}\)
• Entire $s$-harmonic functions are affine
• MULTIVARIATE STABLE FUTURES PRICES
• Asymptotic estimates of multi-dimensional stable densities and their applications
• Regularity theory for fully nonlinear integro-differential equations
• Elliptic Partial Differential Equations of Second Order
• Pointwise estimates for densities of stable semigroups of measures
• Regularity of harmonic functions for anisotropic fractional Laplacians
• Regularity results for nonlocal parabolic equations
• Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian
• Holder estimates for solutions of integro differential equations like the fractional laplace

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