<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-03868496v4</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-01T23:09:28+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Logarithmic Sobolev and interpolation inequalities on the sphere: constructive stability results</title>
            <author role="aut">
              <persName>
                <forename type="first">Giovanni</forename>
                <surname>Brigati</surname>
              </persName>
              <idno type="halauthorid">2655108-0</idno>
              <affiliation ref="#struct-60"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Jean</forename>
                <surname>Dolbeault</surname>
              </persName>
              <email type="md5">3369e41b8636cf57d4d79bbdd1be8c8d</email>
              <email type="domain">ceremade.dauphine.fr</email>
              <idno type="idhal" notation="string">dolbeaul</idno>
              <idno type="idhal" notation="numeric">87</idno>
              <idno type="halauthorid" notation="string">570-87</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/O-2328-2017</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-4234-2298</idno>
              <idno type="IDREF">https://www.idref.fr/120112507</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/http://www.researcherid.com/rid/O-2328-2017</idno>
              <idno type="ARXIV">https://arxiv.org/a/dolbeault_j_1</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=ky2LFVsAAAAJ</idno>
              <affiliation ref="#struct-60"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Nikita</forename>
                <surname>Simonov</surname>
              </persName>
              <email type="md5">32bd665b8e9a0bc28da10cbf14121d23</email>
              <email type="domain">sorbonne-universite.fr</email>
              <idno type="idhal" notation="numeric">1216986</idno>
              <idno type="halauthorid" notation="string">1994923-1216986</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-3241-190X</idno>
              <affiliation ref="#struct-1005052"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Jean</forename>
                <surname>Dolbeault</surname>
              </persName>
              <email type="md5">3369e41b8636cf57d4d79bbdd1be8c8d</email>
              <email type="domain">ceremade.dauphine.fr</email>
            </editor>
            <funder ref="#projanr-43590"/>
            <funder ref="#projeurop-712887"/>
            <funder>Marie Sklodowska-Curie grant agreement n° 754362</funder>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2022-11-23 18:48:50</date>
            </edition>
            <edition n="v2">
              <date type="whenSubmitted">2023-09-30 12:07:44</date>
            </edition>
            <edition n="v3">
              <date type="whenSubmitted">2023-11-23 08:54:52</date>
            </edition>
            <edition n="v4" type="current">
              <date type="whenSubmitted">2024-01-22 22:08:53</date>
              <date type="whenModified">2026-01-03 03:11:25</date>
              <date type="whenReleased">2024-01-24 15:20:37</date>
              <date type="whenProduced">2024</date>
              <date type="whenEndEmbargoed">2024-01-22</date>
              <ref type="file" target="https://hal.science/hal-03868496v4/document">
                <date notBefore="2024-01-22"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-03868496v4/file/BDS2023-Sphere.pdf" id="file-4411002-3831934">
                <date notBefore="2024-01-22"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2211.13180"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="101536">
                <persName>
                  <forename>Jean</forename>
                  <surname>Dolbeault</surname>
                </persName>
                <email type="md5">3369e41b8636cf57d4d79bbdd1be8c8d</email>
                <email type="domain">ceremade.dauphine.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-03868496</idno>
            <idno type="halUri">https://hal.science/hal-03868496</idno>
            <idno type="halBibtex">brigati:hal-03868496</idno>
            <idno type="halRefHtml">&lt;i&gt;Annales de l'Institut Henri Poincaré (C), Analyse non linéaire&lt;/i&gt;, 2024, 41, pp.1289-1321. &lt;a target="_blank" href="https://dx.doi.org/10.4171/AIHPC/106"&gt;&amp;#x27E8;10.4171/AIHPC/106&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Annales de l'Institut Henri Poincaré (C), Analyse non linéaire, 2024, 41, pp.1289-1321. &amp;#x27E8;10.4171/AIHPC/106&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-4411002-3831934"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-DAUPHINE">Université Paris Dauphine - Paris IX</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="CEREMADE" corresp="UNIV-DAUPHINE">CEntre de REcherches en MAthématiques de la DEcision</idno>
            <idno type="stamp" n="LJLL" corresp="SORBONNE-UNIVERSITE">Laboratoire Jacques-Louis Lions</idno>
            <idno type="stamp" n="OPENAIRE">OpenAIRE</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="PSL">Université Paris sciences et lettres</idno>
            <idno type="stamp" n="SORBONNE-UNIVERSITE">Sorbonne Université</idno>
            <idno type="stamp" n="SORBONNE-UNIV" corresp="SORBONNE-UNIVERSITE">Sorbonne Université 01/01/2018</idno>
            <idno type="stamp" n="SU-SCIENCES" corresp="SORBONNE-UNIVERSITE">Faculté des Sciences de Sorbonne Université</idno>
            <idno type="stamp" n="UNIV-PARIS">Université Paris Cité</idno>
            <idno type="stamp" n="UNIVERSITE-PARIS" corresp="UNIV-PARIS">Université Paris Cité</idno>
            <idno type="stamp" n="UP-SCIENCES">Université Paris Cité - Faculté des Sciences</idno>
            <idno type="stamp" n="UNIV-DAUPHINE-PSL" corresp="PSL">Université Paris Dauphine - PSL</idno>
            <idno type="stamp" n="SU-TI">Sorbonne Université - Texte Intégral</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="ALLIANCE-SU"> Alliance Sorbonne Université</idno>
            <idno type="stamp" n="SUPRA_MATHS_INFO">Mathématiques + Informatique</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Logarithmic Sobolev and interpolation inequalities on the sphere: constructive stability results</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Giovanni</forename>
                    <surname>Brigati</surname>
                  </persName>
                  <idno type="halauthorid">2655108-0</idno>
                  <affiliation ref="#struct-60"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Jean</forename>
                    <surname>Dolbeault</surname>
                  </persName>
                  <email type="md5">3369e41b8636cf57d4d79bbdd1be8c8d</email>
                  <email type="domain">ceremade.dauphine.fr</email>
                  <idno type="idhal" notation="string">dolbeaul</idno>
                  <idno type="idhal" notation="numeric">87</idno>
                  <idno type="halauthorid" notation="string">570-87</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/O-2328-2017</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-4234-2298</idno>
                  <idno type="IDREF">https://www.idref.fr/120112507</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/http://www.researcherid.com/rid/O-2328-2017</idno>
                  <idno type="ARXIV">https://arxiv.org/a/dolbeault_j_1</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=ky2LFVsAAAAJ</idno>
                  <affiliation ref="#struct-60"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Nikita</forename>
                    <surname>Simonov</surname>
                  </persName>
                  <email type="md5">32bd665b8e9a0bc28da10cbf14121d23</email>
                  <email type="domain">sorbonne-universite.fr</email>
                  <idno type="idhal" notation="numeric">1216986</idno>
                  <idno type="halauthorid" notation="string">1994923-1216986</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-3241-190X</idno>
                  <affiliation ref="#struct-1005052"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">23058</idno>
                <idno type="issn">0294-1449</idno>
                <idno type="eissn">1873-1430</idno>
                <title level="j">Annales de l'Institut Henri Poincaré (C), Analyse non linéaire</title>
                <imprint>
                  <publisher>EMS</publisher>
                  <biblScope unit="volume">41</biblScope>
                  <biblScope unit="pp">1289–1321</biblScope>
                  <date type="datePub">2024</date>
                </imprint>
              </monogr>
              <idno type="arxiv">2211.13180</idno>
              <idno type="doi">10.4171/AIHPC/106</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">logarithmic Sobolev inequality</term>
                <term xml:lang="en">Gagliardo-Nirenberg inequalities</term>
                <term xml:lang="en">stability</term>
                <term xml:lang="en">sphere</term>
                <term xml:lang="en">spectral decomposition</term>
              </keywords>
              <classCode scheme="classification">26D10; 58J99; 39B62; 43A90; 49J40; 46E35</classCode>
              <classCode scheme="halDomain" n="math.math-ap">Mathematics [math]/Analysis of PDEs [math.AP]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We consider Gagliardo-Nirenberg inequalities on the sphere which interpolate between the Poincaré inequality and the Sobolev inequality, and include the logarithmic Sobolev inequality as a special case. We establish explicit stability results in the subcritical regime using spectral decomposition techniques, and entropy and carré du champ methods applied to nonlinear diffusion flows.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-60" status="VALID">
          <idno type="IdRef">088064239</idno>
          <idno type="ISNI">0000 0004 0645 4046</idno>
          <idno type="RNSR">199712592E</idno>
          <idno type="ROR">https://ror.org/03s0gj002</idno>
          <idno type="Wikidata">Q2913547</idno>
          <orgName>CEntre de REcherches en MAthématiques de la DEcision</orgName>
          <orgName type="acronym">CEREMADE</orgName>
          <date type="start">1971-01-01</date>
          <desc>
            <address>
              <addrLine>Place du Maréchal de Lattre de Tassigny 75775 - Paris Cedex 16</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ceremade.dauphine.fr/index.html</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300302" type="direct"/>
            <relation active="#struct-564132" type="indirect"/>
            <relation name="UMR7534 / URA749" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1005052" status="VALID">
          <idno type="IdRef">099222221</idno>
          <idno type="ISNI">0000000101748385</idno>
          <idno type="RNSR">199712644L</idno>
          <idno type="ROR">https://ror.org/04xmteb38</idno>
          <orgName>Laboratoire Jacques-Louis Lions</orgName>
          <orgName type="acronym">LJLL (UMR_7598)</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>Sorbonne-Université, Boîte courrier 187 - 75252 Paris Cedex 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ljll.math.upmc.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-413221" type="direct"/>
            <relation name="UMR7598" active="#struct-441569" type="direct"/>
            <relation name="UMR_7598" active="#struct-557826" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300302" status="VALID">
          <idno type="IdRef">027787109</idno>
          <idno type="ISNI">0000000120977052</idno>
          <idno type="ROR">https://ror.org/052bz7812</idno>
          <idno type="Wikidata">Q1546437</idno>
          <orgName>Université Paris Dauphine-PSL</orgName>
          <desc>
            <address>
              <addrLine>Place du Maréchal de Lattre de Tassigny75775 PARIS Cedex 16</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://dauphine.psl.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-564132" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-564132" status="VALID">
          <idno type="IdRef">241597595</idno>
          <idno type="ISNI">0000 0004 1784 3645</idno>
          <idno type="ROR">https://ror.org/013cjyk83</idno>
          <orgName>Université Paris Sciences et Lettres</orgName>
          <orgName type="acronym">PSL</orgName>
          <desc>
            <address>
              <addrLine>60 rue Mazarine 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.psl.eu/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-413221" status="VALID">
          <idno type="IdRef">221333754</idno>
          <idno type="ROR">https://ror.org/02en5vm52</idno>
          <orgName>Sorbonne Université</orgName>
          <orgName type="acronym">SU</orgName>
          <date type="start">2018-01-01</date>
          <desc>
            <address>
              <addrLine>21 rue de l’École de médecine - 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.sorbonne-universite.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-557826" status="VALID">
          <idno type="IdRef">236453505</idno>
          <idno type="ISNI">0000 0004 7885 7602</idno>
          <idno type="ROR">https://ror.org/05f82e368</idno>
          <orgName>Université Paris Cité</orgName>
          <orgName type="acronym">UPCité</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>85 boulevard Saint-Germain75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://u-paris.fr/</ref>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-43590" status="VALID">
          <idno type="anr">ANR-17-CE40-0030</idno>
          <orgName>EFI</orgName>
          <desc>Entropie, flots, inégalités</desc>
          <date type="start">2017</date>
        </org>
        <org type="europeanProject" xml:id="projeurop-712887" status="VALID">
          <idno type="number">754362</idno>
          <idno type="program">Increasing structural impact by co-funding activities, EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions</idno>
          <idno type="call">H2020-MSCA-COFUND-2016</idno>
          <orgName>MathInParis</orgName>
          <desc>International Doctoral Training in Mathematical Sciences in Paris</desc>
          <date type="start">2017-09-01</date>
          <date type="end">2023-01-31</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>