Interior Schauder Estimates for Elliptic Equations Associated with Lévy Operators

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

Abstract

We study the local regularity of solutions f to the integro-differential equationAf=ginU for open sets U⊆ ℝd, where A is the infinitesimal generator of a Lévy process (Xt)t≥ 0. Under the assumption that the transition density of (Xt)t≥ 0 satisfies a certain gradient estimate, we establish interior Schauder estimates for both pointwise and weak solutions f. Our results apply for a wide class of Lévy generators, including generators of stable Lévy processes and subordinated Brownian motions.

Details

Original languageEnglish
Pages (from-to)459-481
Number of pages23
JournalPotential Analysis
Volume56 (2022)
Issue number3
Publication statusPublished - 23 Jan 2021
Peer-reviewedYes

Keywords

ASJC Scopus subject areas

Keywords

  • Gradient estimate, Hölder space, Integro-differential equation, Lévy process, Schauder estimate

Library keywords