Weighted Hardy type inequalities with Robin boundary conditions

Ismail Kömbe; Abdullah Yener

doi:10.3934/dcdss.2022195

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2024, Volume 17, Issue 5&6: 1889-1898. Doi: 10.3934/dcdss.2022195

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Weighted Hardy type inequalities with Robin boundary conditions

Ismail Kömbe^1, and
Abdullah Yener^2,

1.
Department of Mechatronics Engineering, Faculty of Engineering, İstanbul Commerce University, Küçükyalı 34840, İstanbul, Türkiye
2.
Department of Mathematics, Faculty of Humanities and Social Sciences, İstanbul Commerce University, Beyoǧlu 34445, İstanbul, Türkiye

Dedicated to Jerry Goldstein on the occasion of his 80th birthday

Received: April 2022

Revised: November 2022

Early access: November 25, 2022

Published online: November 25, 2022

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Abstract

In this paper, we establish a general weighted Hardy type inequality for the $ p- $Laplace operator with Robin boundary condition. We provide various concrete examples to illustrate our results for different weights. Furthermore, we present some Heisenberg-Pauli-Weyl type inequalities with boundary terms on balls centred at the origin with radius $ R $ in $ \mathbb{R} ^n $.

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Mathematics Subject Classification: Primary: 26D10, 35H10; Secondary: 46E35.

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References

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