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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.17249 |
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| _version_ | 1866912673026801664 |
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| author | Chen, Xiao-Ping Tang, Chun-Lei |
| author_facet | Chen, Xiao-Ping Tang, Chun-Lei |
| contents | This paper focuses on remainder estimates of the magnetic $L^p$-Hardy inequalities for $1<p<2$. \emph{Firstly}, we establish a family of remainder terms involving magnetic gradients of the magnetic $L^p$-Hardy inequalities, which are also new even for the classical $L^p$-Hardy inequalities. \emph{Secondly}, we study another family of remainder terms involving logarithmic terms of the magnetic $L^p$-Hardy inequalities. \emph{Lastly}, as a byproduct, we further obtain remainder terms of some other $L^p$-Hardy-type inequalities by using similar proof of our main results.
Furthermore, this paper answers the open question proposed by Cazacu \emph{et al.} in [\emph{Nonlinearity} \textbf{37} (2024), Paper No. 035004] and can be viewed as a supplementary work of it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_17249 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Remainder terms of $L^p$-Hardy inequalities with magnetic fields: the case $1<p<2$ Chen, Xiao-Ping Tang, Chun-Lei Analysis of PDEs This paper focuses on remainder estimates of the magnetic $L^p$-Hardy inequalities for $1<p<2$. \emph{Firstly}, we establish a family of remainder terms involving magnetic gradients of the magnetic $L^p$-Hardy inequalities, which are also new even for the classical $L^p$-Hardy inequalities. \emph{Secondly}, we study another family of remainder terms involving logarithmic terms of the magnetic $L^p$-Hardy inequalities. \emph{Lastly}, as a byproduct, we further obtain remainder terms of some other $L^p$-Hardy-type inequalities by using similar proof of our main results. Furthermore, this paper answers the open question proposed by Cazacu \emph{et al.} in [\emph{Nonlinearity} \textbf{37} (2024), Paper No. 035004] and can be viewed as a supplementary work of it. |
| title | Remainder terms of $L^p$-Hardy inequalities with magnetic fields: the case $1<p<2$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.17249 |