Sharp remainder formulae for general weighted Hardy and Rellich type inequalities for $1<p<\infty$
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| Format: | Preprint |
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2026
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| _version_ | 1866912944280829952 |
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| author | Shaimerdenov, Yerkin Yessirkegenov, Nurgissa Zhangirbayev, Amir |
| author_facet | Shaimerdenov, Yerkin Yessirkegenov, Nurgissa Zhangirbayev, Amir |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_02381 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp remainder formulae for general weighted Hardy and Rellich type inequalities for $1<p<\infty$ Shaimerdenov, Yerkin Yessirkegenov, Nurgissa Zhangirbayev, Amir Analysis of PDEs 26D10, 35J70 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. |
| title | Sharp remainder formulae for general weighted Hardy and Rellich type inequalities for $1<p<\infty$ |
| topic | Analysis of PDEs 26D10, 35J70 |
| url | https://arxiv.org/abs/2603.02381 |