Abstract
We prove Schauder estimates for a class of non-local elliptic operators with kernel K(y) = a(y)/|y|d+σ and either Dini or Hölder continuous data. Here 0 < σ < 2 is a constant and a is a bounded measurable function, which is not necessarily to be homogeneous, regular, or symmetric. As an application, we prove that the operators give isomorphisms between the Lipschitz-Zygmund spaces Λα+σ and Λα for any α > 0. Several local estimates and an extension to operators with kernels K(x, y) are also discussed.
Original language | English |
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Pages (from-to) | 2319-2347 |
Number of pages | 29 |
Journal | Discrete and Continuous Dynamical Systems- Series A |
Volume | 33 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2013 Jun |
Externally published | Yes |
Keywords
- Lévy processes
- Non-local elliptic equations
- Schauder estimates
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics