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

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2018_axioms_djida_interior.pdf (856.32 KB)
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URI: http://hdl.handle.net/10347/23667
E-ISSN: 2075-1680
DOI: 0.3390/axioms7030065

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2018

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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

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Marchaud fractional derivative| Interior regularity| Schauder estimate| Extension problem| Fractional order weighted Sobolev spaces

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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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The second author’s research was supported by a student grant from the Engineering and Physical Sciences Research Council, UK

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© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)
Atribución 4.0 Internacional

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Estatística, Análise Matemática e Optimización