Local Elliptic Regularity for the Dirichlet Fractional Laplacian

Biccari U, Warma M, Zuazua E (2017)

Publication Type: Journal article

Publication year: 2017

Journal

Advanced Nonlinear Studies Uthscsa Press

Book Volume: 17

Pages Range: 387-409

Journal Issue: 2

DOI: 10.1515/ans-2017-0014

Abstract

We prove the Wloc^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. 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.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

University of Deusto / Universidad de Deusto

Spain (ES) University of Puerto Rico (UPR)

Puerto Rico (PR)

How to cite

APA:

Biccari, U., Warma, M., & Zuazua, E. (2017). Local Elliptic Regularity for the Dirichlet Fractional Laplacian. Advanced Nonlinear Studies, 17(2), 387-409. https://dx.doi.org/10.1515/ans-2017-0014

MLA:

Biccari, Umberto, Mahamadi Warma, and Enrique Zuazua. "Local Elliptic Regularity for the Dirichlet Fractional Laplacian." Advanced Nonlinear Studies 17.2 (2017): 387-409.

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