HARDY AND SOBOLEV INEQUALITIES FOR DOUBLE PHASE FUNCTIONALS ON THE UNIT BALL

被引：3
|
作者：
Mizuta, Yoshihiro [1 ]
Shimomura, Tetsu [2 ]
机构：
[1] Hiroshima Univ, Grad Sch Adv Sci & Engn, Higashihiroshima 7398521, Japan
[2] Hiroshima Univ, Grad Sch Humanities & Social Sci, Dept Math, Higashihiroshima 7398521, Japan
来源：
MATHEMATICAL INEQUALITIES & APPLICATIONS | 2022年 / 25卷 / 02期
关键词：
Hardy-Sobolev inequality; double phase functionals; OMEGA-MINIMIZERS; REGULARITY; CALCULUS;
D O I：
10.7153/mia-2022-25-19
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove Hardy and Sobolev inequalities for double phase functionals Phi(x, t) = t(p) + (b(x)t)(q) on the unit ball B, as a continuation of our paper [26], where 1 <= p < q, b(.) is nonnegative and (radially) Holder continuous of order theta is an element of(0,1]. The Sobolev conjugate for Phi is given by Phi*(x, t) = t(p)* +(b(x)t)(q)*, where p* and q* denote the Sobolev exponent of p and q, respectively, that is, 1/p* = 1/p - 1/n and 1/q* = 1/q - 1/n.
引用
收藏
页码：319 / 333
页数：15
相关论文
共 50 条
12345