Local Elliptic Regularity for the Dirichlet Fractional Laplacian
Abstract
We prove the W loc 2 s , p ${W_{{\mathrm{loc}}}^{2s,p}}$ local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian on an arbitrary bounded open set of ℝ N ${\mathbb{R}^{N}}$ . The key tool consists in analyzing carefully the elliptic equation satisfied by the solution locally, after cut-off, to later employ sharp regularity results in the whole space. We do it by two different methods. First working directly in the variational formulation of the elliptic problem and then employing the heat kernel representation of solutions.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Apr 21, 2017
- Source ID
- 10.1515/ans-2017-0014
Entities
People
- Enrique Zuazua
- Mahamadi Warma
- Umberto Biccari
Organizations
- Agence Nationale de la Recherche
- Ministry of Economy, Industry and Competitiveness
- United States Air Force
- University of Puerto Rico