Uniform Poincar\'e inequality in o-minimal structures
Mathematical Inequalities and Applications vol. 26 (2023), 141-150 We first define the trace on a domain $\Omega$ which is definable in an o-minimal structure. We then show that every function $u\in W^{1,p}(\Omega)$ vanishing on the boundary in the trace sense satisfies Poincar\'e inequality. W...
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| creator | Valette, Anna Valette, Guillaume |
| description | Mathematical Inequalities and Applications vol. 26 (2023), 141-150 We first define the trace on a domain $\Omega$ which is definable in an
o-minimal structure. We then show that every function $u\in W^{1,p}(\Omega)$
vanishing on the boundary in the trace sense satisfies Poincar\'e inequality.
We finally show, given a definable family of domains $(\Omega_t)_{t\in
\mathbb{R}^k}$, that the constant of this inequality remains bounded, if so
does the volume of $\Omega_t$. |
| doi_str_mv | 10.48550/arxiv.2111.05019 |
| format | Article |
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o-minimal structure. We then show that every function $u\in W^{1,p}(\Omega)$
vanishing on the boundary in the trace sense satisfies Poincar\'e inequality.
We finally show, given a definable family of domains $(\Omega_t)_{t\in
\mathbb{R}^k}$, that the constant of this inequality remains bounded, if so
does the volume of $\Omega_t$.</description><identifier>DOI: 10.48550/arxiv.2111.05019</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs</subject><creationdate>2021-11</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/2111.05019$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2111.05019$$DView paper in arXiv$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.7153/mia-2023-26-11$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink></links><search><creatorcontrib>Valette, Anna</creatorcontrib><creatorcontrib>Valette, Guillaume</creatorcontrib><title>Uniform Poincar\'e inequality in o-minimal structures</title><description>Mathematical Inequalities and Applications vol. 26 (2023), 141-150 We first define the trace on a domain $\Omega$ which is definable in an
o-minimal structure. We then show that every function $u\in W^{1,p}(\Omega)$
vanishing on the boundary in the trace sense satisfies Poincar\'e inequality.
We finally show, given a definable family of domains $(\Omega_t)_{t\in
\mathbb{R}^k}$, that the constant of this inequality remains bounded, if so
does the volume of $\Omega_t$.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNpjYJA0NNAzsTA1NdBPLKrILNMzMjQ01DMwNTC05GQwDc3LTMsvylUIyM_MS04silFPVcjMSy0sTczJLKkEMhXydXMz8zJzE3MUikuKSpNLSotSi3kYWNMSc4pTeaE0N4O8m2uIs4cu2IL4giKg-qLKeJBF8WCLjAmrAAB7SzLc</recordid><startdate>20211109</startdate><enddate>20211109</enddate><creator>Valette, Anna</creator><creator>Valette, Guillaume</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20211109</creationdate><title>Uniform Poincar\'e inequality in o-minimal structures</title><author>Valette, Anna ; Valette, Guillaume</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2111_050193</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Valette, Anna</creatorcontrib><creatorcontrib>Valette, Guillaume</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Valette, Anna</au><au>Valette, Guillaume</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Uniform Poincar\'e inequality in o-minimal structures</atitle><date>2021-11-09</date><risdate>2021</risdate><abstract>Mathematical Inequalities and Applications vol. 26 (2023), 141-150 We first define the trace on a domain $\Omega$ which is definable in an
o-minimal structure. We then show that every function $u\in W^{1,p}(\Omega)$
vanishing on the boundary in the trace sense satisfies Poincar\'e inequality.
We finally show, given a definable family of domains $(\Omega_t)_{t\in
\mathbb{R}^k}$, that the constant of this inequality remains bounded, if so
does the volume of $\Omega_t$.</abstract><doi>10.48550/arxiv.2111.05019</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs |
| title | Uniform Poincar\'e inequality in o-minimal structures |
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