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Regularity theory for general stable operators

Author
Ros, X.; Serra, J.
Type of activity
Journal article
Journal
Journal of differential equations
Date of publication
2016-06-15
Volume
260
Number
12
First page
8675
Last page
8715
DOI
https://doi.org/10.1016/j.jde.2016.02.033 Open in new window
Project funding
Partial Differential Equations: reaction-diffusion, integro-differential, and geometric problems
URL
http://www.sciencedirect.com/science/article/pii/S0022039616000991 Open in new window
Abstract
We establish sharp regularity estimates for solutions to Lu = f in Omega subset of R-n being the generator of any stable and symmetric Levy process. Such nonlocal operators L depend on a finite measure on Sn-1, called the spectral measure.; First, we study the interior regularity of solutions to Lu = f in B-1. We prove that if f is C-alpha then u belong to C alpha+2s whenever alpha + 2s is not an integer. In case f is an element of L-infinity we show that the solution u is C-2s when s not equal ...
Keywords
BEHAVIOR, BOUNDARY, Boundary regularity, DENSITIES, FRACTIONAL LAPLACIANS, HARMONIC-FUNCTIONS, HARNACKS INEQUALITY, INTEGRODIFFERENTIAL EQUATIONS, Interior regularity, JUMP-PROCESSES, MU-TRANSMISSION, SEMIGROUPS, Stable Levy processes
Group of research
EDP - Partial Differential Equations and Applications

Participants

  • Ros Oton, Xavier  (author)
  • Serra Montoli, Joaquim  (author)