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.

引用

页数：16

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