Reverse Poincare-type inequalities for the difference of superharmonic functions

被引：2

作者：

Pecaric, Josip ^{[1
]}

Saleem, Muhammad Shoaib ^{[2
]}

Rehman, Hamood Ur ^{[2
]}

Nizami, Abdul Majeed ^{[2
]}

Hussain, Abid ^{[2
]}

机构：

[1] Univ Zagreb, Fac Text Technol, Zagreb 10000, Croatia

[2] Univ Educ, Dept Math, Lahore, Pakistan

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2015年

关键词：

concave functions; superharmonic functions; weak derivative; weight function; compact support; weak superharmonic function; superharmonic majorants;

D O I：

10.1186/s13660-015-0916-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we develop the weighted square integral inequalities for the difference of two smooth superharmonic functions. Then we prove the existence and integrability of the Sobolev derivative for superharmonic functions. The inequalities are generalized for the difference of two weak superharmonic functions. We also establish that the superharmonic approximation is indeed the better imitation of the exact unknown solution rather than the usual uniform approximation.

引用

页码：1 / 11

页数：11

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