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

被引：3
|
作者：
Djida, Jean-Daniel [1 ]
Fernandez, Arran [2 ]
机构：
[1] Univ Santiago de Compostela, Dept Anal Matemat, Santiago De Compostela 15782, Spain
[2] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 0WA, England
来源：
AXIOMS | 2018年 / 7卷 / 03期
基金：
英国工程与自然科学研究理事会;
关键词：
marchaud fractional derivative; interior regularity; schauder estimate; extension problem; fractional order weighted Sobolev spaces;
D O I：
10.3390/axioms7030065
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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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页数：16
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