Back to Search
Start Over
The Dirichlet problem for nonlocal operators with kernels: Convex and nonconvex domains
- Publication Year :
- 2015
- Publisher :
- Weierstrass Institute, 2015.
-
Abstract
- We study the interior regularity of solutions to a Dirichlet problem for anisotropic operators of fractional type. A prototype example is given by the sum of one-dimensional fractional Laplacians in fixed, given directions. We prove here that an interior differentiable regularity theory holds in convex domains. When the spectral measure is a bounded function and the domain is smooth, the same regularity theory applies. In particular, solutions always possess a classical first derivative. The assumptions on the domain are sharp, since if the domain is not convex and the spectral measure is singular, we construct an explicit counterexample.
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....2176381802a2d3fb31e21ad5ef1b7300
- Full Text :
- https://doi.org/10.20347/wias.preprint.2076