Domain characterization for Schr\"odinger operators with sub-quadratic singularity
We characterize the domain of the Schr\"odinger operators $S=-\Delta+c|x|^{-\alpha}$ in $L^p(\mathbb{R}^N)$, with $0
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| creator | Metafune, Giorgio Sobajima, Motohiro |
| description | We characterize the domain of the Schr\"odinger operators
$S=-\Delta+c|x|^{-\alpha}$ in $L^p(\mathbb{R}^N)$, with $0 |
| doi_str_mv | 10.48550/arxiv.2409.09917 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2409_09917</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2409_09917</sourcerecordid><originalsourceid>FETCH-arxiv_primary_2409_099173</originalsourceid><addsrcrecordid>eNqFjrsOgkAQRbexMOoHWDmxB1eFKLWPWKulCRmXRSYBFmcXFb9eJPZWN7k5yTlCjOfSD9ZhKGfIL3r4i0BGvoyi-aovjltTIJWgMmRUTjO90ZEpITUMJ5XxZWoSKm-awVSa0Rm28CSXga2v3r3GpP1IgW2ZOkcm1wxFL8Xc6tFvB2Ky3503B6-zxxVTgdzE34q4q1j-Jz4W0j6s</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Domain characterization for Schr\"odinger operators with sub-quadratic singularity</title><source>arXiv.org</source><creator>Metafune, Giorgio ; Sobajima, Motohiro</creator><creatorcontrib>Metafune, Giorgio ; Sobajima, Motohiro</creatorcontrib><description>We characterize the domain of the Schr\"odinger operators
$S=-\Delta+c|x|^{-\alpha}$ in $L^p(\mathbb{R}^N)$, with $0<\alpha<2$ and
$c\in\mathbb{R}$. When $\alpha p< N$, the domain characterization is
essentially known and can be proved using different tools, for instance kernel
estimates and potentials in the Kato class or in the reverse H\"older class.
However,the other cases seem not to be known, so far.In this paper, we give the
explicit description of the domain of $S$ for all range of parameters
$p,\alpha$ and $c$.</description><identifier>DOI: 10.48550/arxiv.2409.09917</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs</subject><creationdate>2024-09</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2409.09917$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2409.09917$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Metafune, Giorgio</creatorcontrib><creatorcontrib>Sobajima, Motohiro</creatorcontrib><title>Domain characterization for Schr\"odinger operators with sub-quadratic singularity</title><description>We characterize the domain of the Schr\"odinger operators
$S=-\Delta+c|x|^{-\alpha}$ in $L^p(\mathbb{R}^N)$, with $0<\alpha<2$ and
$c\in\mathbb{R}$. When $\alpha p< N$, the domain characterization is
essentially known and can be proved using different tools, for instance kernel
estimates and potentials in the Kato class or in the reverse H\"older class.
However,the other cases seem not to be known, so far.In this paper, we give the
explicit description of the domain of $S$ for all range of parameters
$p,\alpha$ and $c$.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNqFjrsOgkAQRbexMOoHWDmxB1eFKLWPWKulCRmXRSYBFmcXFb9eJPZWN7k5yTlCjOfSD9ZhKGfIL3r4i0BGvoyi-aovjltTIJWgMmRUTjO90ZEpITUMJ5XxZWoSKm-awVSa0Rm28CSXga2v3r3GpP1IgW2ZOkcm1wxFL8Xc6tFvB2Ky3503B6-zxxVTgdzE34q4q1j-Jz4W0j6s</recordid><startdate>20240915</startdate><enddate>20240915</enddate><creator>Metafune, Giorgio</creator><creator>Sobajima, Motohiro</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20240915</creationdate><title>Domain characterization for Schr\"odinger operators with sub-quadratic singularity</title><author>Metafune, Giorgio ; Sobajima, Motohiro</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2409_099173</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Metafune, Giorgio</creatorcontrib><creatorcontrib>Sobajima, Motohiro</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Metafune, Giorgio</au><au>Sobajima, Motohiro</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Domain characterization for Schr\"odinger operators with sub-quadratic singularity</atitle><date>2024-09-15</date><risdate>2024</risdate><abstract>We characterize the domain of the Schr\"odinger operators
$S=-\Delta+c|x|^{-\alpha}$ in $L^p(\mathbb{R}^N)$, with $0<\alpha<2$ and
$c\in\mathbb{R}$. When $\alpha p< N$, the domain characterization is
essentially known and can be proved using different tools, for instance kernel
estimates and potentials in the Kato class or in the reverse H\"older class.
However,the other cases seem not to be known, so far.In this paper, we give the
explicit description of the domain of $S$ for all range of parameters
$p,\alpha$ and $c$.</abstract><doi>10.48550/arxiv.2409.09917</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs |
| title | Domain characterization for Schr\"odinger operators with sub-quadratic singularity |
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