Interior and boundary regularity results for strongly nonhomogeneous p, q-fractional problems

被引：13

作者：

Giacomoni, Jacques ^{[1
]}

Kumar, Deepak ^{[2
]}

Sreenadh, Konijeti ^{[2
]}

机构：

[1] Univ Pau & Pays Adour, LMAP UMR E2S UPPA CNRS 5142, Bat IPRA,Ave Univ, F-64013 Pau, France

[2] Indian Inst Technol Delhi, Dept Math, New Delhi 110016, India

来源：

ADVANCES IN CALCULUS OF VARIATIONS | 2021年

关键词：

Fractional; (p; q)-Laplacian; nonhomogeneous nonlocal operator; singular nonlinearity; local and boundary Holder continuity; maximum principle; strong comparison principle; HOLDER REGULARITY; NONLOCAL PROBLEMS; EQUATIONS; MULTIPLICITY; LAPLACIAN; SOBOLEV;

D O I：

10.1515/acv-2021-0040

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we deal with the global regularity of weak solutions to a class of problems involving the fractional (p, q)-Laplacian, denoted by (-Delta)(p)(s1) + (-Delta)(q)(s2) for s(2), s(1) is an element of (0, 1) and 1 < p, q < infinity. We establish completely new Holder continuity results, up to the boundary, for the weak solutions to fractional ( p, q)-problems involving singular as well as regular nonlinearities. Moreover, as applications to boundary estimates, we establish a new Hopf-type maximum principle and a strong comparison principle in both situations.

引用

页码：467 / 501

页数：35

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