Integral representation of solutions using Green function for fractional Hardy equations

被引：9

作者：

Bhakta, Mousomi ^{[1
]}

Biswas, Anup ^{[1
]}

Ganguly, Debdip ^{[1
]}

Montoro, Luigi ^{[2
]}

机构：

[1] Indian Inst Sci Educ & Res, Dept Math, Dr Homi Bhaba Rd, Pune 411008, Maharashtra, India

[2] Unical, Dipartimento Matemat & Informat, Ponte Pietro Bucci 31 B, I-87036 Cosenza, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 269卷 / 07期

关键词：

Fractional Laplacian; Hardy operator; Green function; Integral representation; Hardy equation; Semigroup; INEQUALITIES; OPERATORS;

D O I：

10.1016/j.jde.2020.04.022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Our main aim is to study Green function for the fractional Hardy operator P := (-Delta)(s) - theta/vertical bar x vertical bar(2s) in R-N, where 0 < theta< Lambda(Ns) and Lambda(N,s) is the best constant in the fractional Hardy inequality. Using Green function, we also show that the integral representation of the weak solution holds. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：5573 / 5594

页数：22