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
收藏
页数：16
相关论文
共 50 条
  • [1] BOUNDARY REGULARITY FOR A DEGENERATE ELLIPTIC EQUATION WITH MIXED BOUNDARY CONDITIONS
    Niang, Alassane
    [J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2019, 18 (01) : 107 - 128
  • [2] LOW REGULARITY ESTIMATES FOR CUTFEM APPROXIMATIONS OF AN ELLIPTIC PROBLEM WITH MIXED BOUNDARY CONDITIONS
    Burman, Erik
    Hansbo, Peter
    Larson, Mats G.
    [J]. MATHEMATICS OF COMPUTATION, 2023, : 35 - 54
  • [3] Optimal Regularity of a Degenerate Elliptic Equation
    Wang, Xiaohuan
    Zhang, Jihui
    [J]. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2023, 30 (01) : 254 - 268
  • [4] Optimal Regularity of a Degenerate Elliptic Equation
    Xiaohuan Wang
    Jihui Zhang
    [J]. Journal of Nonlinear Mathematical Physics, 2023, 30 : 254 - 268
  • [5] Some remarks on interior elliptic regularity estimates
    Behzadan, A.
    [J]. JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS, 2021, 7 (01) : 137 - 169
  • [6] Boundary Estimates for a Degenerate Parabolic Equation with Partial Dirichlet Boundary Conditions
    Epstein, Charles L.
    Pop, Camelia A.
    [J]. JOURNAL OF GEOMETRIC ANALYSIS, 2020, 30 (03) : 2377 - 2421
  • [7] Boundary Estimates for a Degenerate Parabolic Equation with Partial Dirichlet Boundary Conditions
    Charles L. Epstein
    Camelia A. Pop
    [J]. The Journal of Geometric Analysis, 2020, 30 : 2377 - 2421
  • [8] A Solution of a Boundary Value Problem with Mixed Conditions for a Four-Dimensional Degenerate Elliptic Equation
    Baishemirov, Zharasbek
    Berdyshev, Abdumauvlen
    Ryskan, Ainur
    [J]. MATHEMATICS, 2022, 10 (07)
  • [9] Interior regularity results for fractional elliptic equations that degenerate with the gradient
    dos Prazeres, Disson
    Topp, Erwin
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 300 : 814 - 829
  • [10] Interior Regularity for Degenerate Elliptic Equations with Drift on Homogeneous Groups
    Feng, Xiaojing
    Niu, Pengcheng
    [J]. JOURNAL OF LIE THEORY, 2013, 23 (03) : 803 - 825
12345