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arXiv · 2603.02381

Sharp remainder formulae for general weighted Hardy and Rellich type inequalities for $1<p<\infty$

Yerkin Shaimerdenov·Nurgissa Yessirkegenov·Amir Zhangirbayev
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Abstract

Inspired by the work of Cossetti and D'Arca [CD25], we show that the general weighted $L^{p}$-Hardy type inequalities [CD25, Theorems 1.1 and 1.2] and the corresponding identities hold for all $1<p<\infty$, thus extending their results beyond the case $p\geq 2$. In addition, we present a general weighted $L^{p}$-Rellich type inequality with a sharp remainder term for quasilinear second order degenerate elliptic differential operators. In particular, even for the classical Laplacian, these identities appear to be new.

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Yerkin Shaimerdenov, Nurgissa Yessirkegenov, Amir Zhangirbayev. 2026-03-02. Sharp remainder formulae for general weighted Hardy and Rellich type inequalities for $1<p<\infty$. https://arxiv.org/abs/2603.02381

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