On Weak and Viscosity Solutions of Nonlocal Double Phase Equations

被引：17
作者：
Fang, Yuzhou [1 ]
Zhang, Chao [1 ,2 ]
机构：
[1] Harbin Inst Technol, Sch Math, Harbin 150001, Peoples R China
[2] Harbin Inst Technol, Inst Adv Study Math, Harbin 150001, Peoples R China
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2021年
基金：
中国国家自然科学基金;
关键词：
FRACTIONAL P-LAPLACIAN; HOLDER REGULARITY; MINIMIZERS;
D O I：
10.1093/imrn/rnab351
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the nonlocal double phase equation P.V. integral(Rn) vertical bar u(x) - u(Y)(p-2)(u(x)) - u(y))K-sp(X,Y)dY + P.V. integral(Rn) a(x,y)vertical bar u(x) - u(Y)vertical bar(q-2)(u(X) - u(Y))K-tq(X,Y) dY = 0 where 1 < p <= q and the modulating coefficient a(. , .) >= 0. Under some suitable hypotheses, we first use the De Giorgi-Nash-Moser methods to derive the local Holder continuity for bounded weak solutions and then establish the relationship between weak solutions and viscosity solutions to such equations.
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页码：3746 / 3789
页数：44
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