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Accessible Unlicensed Requires Authentication Published by De Gruyter July 19, 2019

A geometrical version of Hardy-Rellich type inequalities

Ramil Nasibullin
From the journal Mathematica Slovaca

Abstract

We obtained a version of Hardy-Rellich type inequality in a domain Ω ∈ ℝn which involves the distance to the boundary, the diameter and the volume of Ω. Weight functions in the inequalities depend on the “mean-distance” function and on the distance function to the boundary of Ω. The proved inequalities connect function to first and second order derivatives.

MSC 2010: Primary 26D10; 26D15

  1. (Communicated by Ján Borsík )

Acknowledgements

The author thanks Professor F. G. Avkhadiev for constant attention to this work.

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Received: 2018-08-14
Accepted: 2018-12-16
Published Online: 2019-07-19
Published in Print: 2019-08-27

© 2019 Mathematical Institute Slovak Academy of Sciences