Weighted and anisotropic Sobolev inequality with extremal

被引：10

作者：

Bal, Kaushik ^{[1
]}

Garain, Prashanta ^{[2
]}

机构：

[1] Indian Inst Technol, Dept Math & Stat, Kanpur 208016, Uttar Pradesh, India

[2] Ben Gurian Univ Negev, Dept Math, POB 653, IL-8410501 Beer Sheva, Israel

来源：

MANUSCRIPTA MATHEMATICA | 2022年 / 168卷 / 1-2期

关键词：

35A23; 35J62; 35J70; 35J75;

D O I：

10.1007/s00229-021-01298-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a bounded smooth domain Omega subset of R-N with N >= 2, we establish a weighted and an anisotropic version of Sobolev inequality related to the embedding W-0(1,p)(Omega)hooked right arrow L-q(Omega) for 1<p<infinity and 2 <= p<infinity respectively. Our main emphasize is the case of 0<q<1 and we deal with a class of Muckenhoupt weights. Moreover, we obtain existence results for weighted and anisotropic p-Laplace equation with mixed singular nonlinearities and observe that the extremals of our inequalities are associated to such singular problems.

引用

页码：101 / 117

页数：17

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