Heat and Martin kernel estimates for Schr\"{o}dinger operators with critical Hardy potentials
Let $\Omega$ be a bounded domain in $\mathbb{R}^N$ with $C^2$ boundary and let $K\subset\partial\Omega$ be either a $C^2$ submanifold of the boundary of codimension $k
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Barbatis, Gerassimos Gkikas, Konstantinos T Tertikas, Achilles |
| description | Let $\Omega$ be a bounded domain in $\mathbb{R}^N$ with $C^2$ boundary and
let $K\subset\partial\Omega$ be either a $C^2$ submanifold of the boundary of
codimension $k |
| doi_str_mv | 10.48550/arxiv.2207.04667 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2207_04667</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2207_04667</sourcerecordid><originalsourceid>FETCH-arxiv_primary_2207_046673</originalsourceid><addsrcrecordid>eNqFzj0PwVAUxvG7GAQfwOTErqr6YhfSxcRImpP2VG_Uvc25J2jEd1diN_2XJ3l-So0XvheuosifIz_0zQsCP_H8MI6TvjqlhAJoCtghizZwITZUAznRVxRyUFqGfV7xcfq0r0KbMzHYhhjFsoO7lgpy1qJzrCFFLlporJARjbUbql7ZhUa_DtRkuzms09kXkjXcfXCbfUDZF7T8v3gDySJCHQ</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Heat and Martin kernel estimates for Schr\"{o}dinger operators with critical Hardy potentials</title><source>arXiv.org</source><creator>Barbatis, Gerassimos ; Gkikas, Konstantinos T ; Tertikas, Achilles</creator><creatorcontrib>Barbatis, Gerassimos ; Gkikas, Konstantinos T ; Tertikas, Achilles</creatorcontrib><description>Let $\Omega$ be a bounded domain in $\mathbb{R}^N$ with $C^2$ boundary and
let $K\subset\partial\Omega$ be either a $C^2$ submanifold of the boundary of
codimension $k<N$ or a point. In this article we study various problems related
to the Schr\"odinger operator $L_{\mu} =-\Delta - \mu d_K^{-2}$ where $d_K$
denotes the distance to $K$ and $\mu\leq k^2/4$. We establish parabolic
boundary Harnack inequalities as well as related two-sided heat kernel and
Green function estimates. We construct the associated Martin kernel and prove
existence and uniqueness for the corresponding boundary value problem with data
given by measures. Next we apply the results to the study of $L_\mu u+g(u) = 0$
and establish existence and uniqueness under suitable assumptions on the
function $g$. To prove our results we introduce among other things a suitable
notion of boundary trace. This trace is different from the one used by Marcus
and Nguyen \cite{MT} thus allowing us to cover the whole range $\mu\leq k^2/4$.</description><identifier>DOI: 10.48550/arxiv.2207.04667</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs</subject><creationdate>2022-07</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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,781,886</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2207.04667$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2207.04667$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Barbatis, Gerassimos</creatorcontrib><creatorcontrib>Gkikas, Konstantinos T</creatorcontrib><creatorcontrib>Tertikas, Achilles</creatorcontrib><title>Heat and Martin kernel estimates for Schr\"{o}dinger operators with critical Hardy potentials</title><description>Let $\Omega$ be a bounded domain in $\mathbb{R}^N$ with $C^2$ boundary and
let $K\subset\partial\Omega$ be either a $C^2$ submanifold of the boundary of
codimension $k<N$ or a point. In this article we study various problems related
to the Schr\"odinger operator $L_{\mu} =-\Delta - \mu d_K^{-2}$ where $d_K$
denotes the distance to $K$ and $\mu\leq k^2/4$. We establish parabolic
boundary Harnack inequalities as well as related two-sided heat kernel and
Green function estimates. We construct the associated Martin kernel and prove
existence and uniqueness for the corresponding boundary value problem with data
given by measures. Next we apply the results to the study of $L_\mu u+g(u) = 0$
and establish existence and uniqueness under suitable assumptions on the
function $g$. To prove our results we introduce among other things a suitable
notion of boundary trace. This trace is different from the one used by Marcus
and Nguyen \cite{MT} thus allowing us to cover the whole range $\mu\leq k^2/4$.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNqFzj0PwVAUxvG7GAQfwOTErqr6YhfSxcRImpP2VG_Uvc25J2jEd1diN_2XJ3l-So0XvheuosifIz_0zQsCP_H8MI6TvjqlhAJoCtghizZwITZUAznRVxRyUFqGfV7xcfq0r0KbMzHYhhjFsoO7lgpy1qJzrCFFLlporJARjbUbql7ZhUa_DtRkuzms09kXkjXcfXCbfUDZF7T8v3gDySJCHQ</recordid><startdate>20220711</startdate><enddate>20220711</enddate><creator>Barbatis, Gerassimos</creator><creator>Gkikas, Konstantinos T</creator><creator>Tertikas, Achilles</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220711</creationdate><title>Heat and Martin kernel estimates for Schr\"{o}dinger operators with critical Hardy potentials</title><author>Barbatis, Gerassimos ; Gkikas, Konstantinos T ; Tertikas, Achilles</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2207_046673</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Barbatis, Gerassimos</creatorcontrib><creatorcontrib>Gkikas, Konstantinos T</creatorcontrib><creatorcontrib>Tertikas, Achilles</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Barbatis, Gerassimos</au><au>Gkikas, Konstantinos T</au><au>Tertikas, Achilles</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Heat and Martin kernel estimates for Schr\"{o}dinger operators with critical Hardy potentials</atitle><date>2022-07-11</date><risdate>2022</risdate><abstract>Let $\Omega$ be a bounded domain in $\mathbb{R}^N$ with $C^2$ boundary and
let $K\subset\partial\Omega$ be either a $C^2$ submanifold of the boundary of
codimension $k<N$ or a point. In this article we study various problems related
to the Schr\"odinger operator $L_{\mu} =-\Delta - \mu d_K^{-2}$ where $d_K$
denotes the distance to $K$ and $\mu\leq k^2/4$. We establish parabolic
boundary Harnack inequalities as well as related two-sided heat kernel and
Green function estimates. We construct the associated Martin kernel and prove
existence and uniqueness for the corresponding boundary value problem with data
given by measures. Next we apply the results to the study of $L_\mu u+g(u) = 0$
and establish existence and uniqueness under suitable assumptions on the
function $g$. To prove our results we introduce among other things a suitable
notion of boundary trace. This trace is different from the one used by Marcus
and Nguyen \cite{MT} thus allowing us to cover the whole range $\mu\leq k^2/4$.</abstract><doi>10.48550/arxiv.2207.04667</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.2207.04667 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_2207_04667 |
| source | arXiv.org |
| subjects | Mathematics - Analysis of PDEs |
| title | Heat and Martin kernel estimates for Schr\"{o}dinger operators with critical Hardy potentials |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-15T05%3A53%3A37IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Heat%20and%20Martin%20kernel%20estimates%20for%20Schr%5C%22%7Bo%7Ddinger%20operators%20with%20critical%20Hardy%20potentials&rft.au=Barbatis,%20Gerassimos&rft.date=2022-07-11&rft_id=info:doi/10.48550/arxiv.2207.04667&rft_dat=%3Carxiv_GOX%3E2207_04667%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |