Higher Holder regularity for mixed local and nonlocal degenerate elliptic equations

被引：28
|
作者：
Garain, Prashanta [1 ,3 ]
Lindgren, Erik [2 ]
机构：
[1] Uppsala Univ, Dept Math, Box 480, S-75106 Uppsala, Sweden
[2] KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden
[3] Indian Inst Technol Indore, Dept Math, Khandwa Rd, Simrol 453552, Madhya Pradesh, India
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 62卷 / 02期
基金：
瑞典研究理事会;
关键词：
35B65; 35D30; 35J70; 35R09; 35R11; HARNACK PRINCIPLE; DIRICHLET FORMS; P-LAPLACIAN;
D O I：
10.1007/s00526-022-02401-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider equations involving a combination of local and nonlocal degenerate p-Laplace operators. The main contribution of the paper is almost Lipschitz regularity for the homogeneous equation and Holder continuity with an explicit Holder exponent in the general case. For certain parameters, our results also imply Holder continuity of the gradient. In addition, we establish existence, uniqueness and local boundedness. The approach is based on an iteration in the spirit of Moser combined with an approximation method.
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页数：36
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