Interior Regularity Estimates for a Degenerate Elliptic Equation with Mixed Boundary Conditions
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 ellipti...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-09-01
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| Series: | Axioms |
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| Online Access: | http://www.mdpi.com/2075-1680/7/3/65 |
| _version_ | 1818042299621310464 |
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| author | Jean-Daniel Djida Arran Fernandez |
| author_facet | Jean-Daniel Djida Arran Fernandez |
| author_sort | Jean-Daniel Djida |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T08:44:07Z |
| format | Article |
| id | doaj.art-79110f3e9f114d47bfb9553719257589 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-10T08:44:07Z |
| publishDate | 2018-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-79110f3e9f114d47bfb95537192575892022-12-22T01:55:47ZengMDPI AGAxioms2075-16802018-09-01736510.3390/axioms7030065axioms7030065Interior Regularity Estimates for a Degenerate Elliptic Equation with Mixed Boundary ConditionsJean-Daniel Djida0Arran Fernandez1Departamento de Análise Matemática, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, SpainDepartment of Applied Mathematics & Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UKThe 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.http://www.mdpi.com/2075-1680/7/3/65marchaud fractional derivativeinterior regularityschauder estimateextension problemfractional order weighted Sobolev spaces |
| spellingShingle | Jean-Daniel Djida Arran Fernandez Interior Regularity Estimates for a Degenerate Elliptic Equation with Mixed Boundary Conditions Axioms marchaud fractional derivative interior regularity schauder estimate extension problem fractional order weighted Sobolev spaces |
| title | Interior Regularity Estimates for a Degenerate Elliptic Equation with Mixed Boundary Conditions |
| title_full | Interior Regularity Estimates for a Degenerate Elliptic Equation with Mixed Boundary Conditions |
| title_fullStr | Interior Regularity Estimates for a Degenerate Elliptic Equation with Mixed Boundary Conditions |
| title_full_unstemmed | Interior Regularity Estimates for a Degenerate Elliptic Equation with Mixed Boundary Conditions |
| title_short | Interior Regularity Estimates for a Degenerate Elliptic Equation with Mixed Boundary Conditions |
| title_sort | interior regularity estimates for a degenerate elliptic equation with mixed boundary conditions |
| topic | marchaud fractional derivative interior regularity schauder estimate extension problem fractional order weighted Sobolev spaces |
| url | http://www.mdpi.com/2075-1680/7/3/65 |
| work_keys_str_mv | AT jeandanieldjida interiorregularityestimatesforadegenerateellipticequationwithmixedboundaryconditions AT arranfernandez interiorregularityestimatesforadegenerateellipticequationwithmixedboundaryconditions |