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Axioms 2018, 7(3), 65; https://doi.org/10.3390/axioms7030065

Interior Regularity Estimates for a Degenerate Elliptic Equation with Mixed Boundary Conditions

1
Departamento de Análise Matemática, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
2
Department of Applied Mathematics & Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
*
Author to whom correspondence should be addressed.
Received: 9 August 2018 / Revised: 24 August 2018 / Accepted: 27 August 2018 / Published: 1 September 2018
(This article belongs to the Special Issue Mathematical Analysis and Applications)
Full-Text   |   PDF [856 KB, uploaded 3 September 2018]

Abstract

The Marchaud fractional derivative can be obtained as a Dirichlet-to–Neumann map via an extension problem to the upper half space. In this paper we prove interior Schauder regularity estimates for a degenerate elliptic equation with mixed Dirichlet–Neumann boundary conditions. The degenerate elliptic equation arises from the Bernardis–Reyes–Stinga–Torrea extension of the Dirichlet problem for the Marchaud fractional derivative. View Full-Text
Keywords: marchaud fractional derivative; interior regularity; schauder estimate; extension problem; fractional order weighted Sobolev spaces marchaud fractional derivative; interior regularity; schauder estimate; extension problem; fractional order weighted Sobolev spaces
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Djida, J.-D.; Fernandez, A. Interior Regularity Estimates for a Degenerate Elliptic Equation with Mixed Boundary Conditions. Axioms 2018, 7, 65.

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