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2015•Journal of Inequalities and ApplicationsOpen access

Reverse Poincaré-type inequalities for the difference of superharmonic functions

‎Josip Pečarić, Muhammad Shoaib Saleem, Hamood Ur Rehman, Abdul Majeed Nizami, Abid Hussain

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Abstract

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.

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What this paper is about

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.

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Available abstract

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.

Key concepts: Subharmonic function, Mathematics, Inequality, Mathematical analysis, Type (biology), Pure mathematics, Square (algebra), Applied mathematics

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