<?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-00600940</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="2026-05-14T14:51:19+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Inverse problems for the Schrödinger equation via Carleman inequalities with degenerate weights</title>
            <author role="aut">
              <persName>
                <forename type="first">Alberto</forename>
                <surname>Mercado</surname>
              </persName>
              <email type="md5">e5804d0ec247e93c8a54aa3c4fc1d1ed</email>
              <email type="domain">dim.uchile.cl</email>
              <idno type="idhal" notation="numeric">848387</idno>
              <idno type="halauthorid" notation="string">11172-848387</idno>
              <affiliation ref="#struct-1812"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Axel</forename>
                <surname>Osses</surname>
              </persName>
              <idno type="halauthorid">177185-0</idno>
              <affiliation ref="#struct-40802"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Lionel</forename>
                <surname>Rosier</surname>
              </persName>
              <email type="md5">c65833548ab0b6bf44700b3353efff83</email>
              <email type="domain">univ-littoral.fr</email>
              <idno type="idhal" notation="string">lionel-rosier</idno>
              <idno type="idhal" notation="numeric">14724</idno>
              <idno type="halauthorid" notation="string">2813-14724</idno>
              <idno type="IDREF">https://www.idref.fr/081301146</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-5602-9799</idno>
              <idno type="GOOGLE SCHOLAR">deLqIscAAAAJ&amp;hl=fr</idno>
              <idno type="ISNI">http://isni.org/isni/0000000114928094</idno>
              <idno type="VIAF">https://viaf.org/viaf/64894912</idno>
              <affiliation ref="#struct-23"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Lionel</forename>
                <surname>Rosier</surname>
              </persName>
              <email type="md5">c65833548ab0b6bf44700b3353efff83</email>
              <email type="domain">univ-littoral.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2011-06-16 11:23:14</date>
              <date type="whenModified">2025-11-04 12:02:09</date>
              <date type="whenReleased">2011-06-16 11:23:14</date>
              <date type="whenProduced">2008</date>
              <ref type="externalLink" target="http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&amp;idBib=3263553"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="147930">
                <persName>
                  <forename>Lionel</forename>
                  <surname>Rosier</surname>
                </persName>
                <email type="md5">c65833548ab0b6bf44700b3353efff83</email>
                <email type="domain">univ-littoral.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00600940</idno>
            <idno type="halUri">https://hal.science/hal-00600940</idno>
            <idno type="halBibtex">mercado:hal-00600940</idno>
            <idno type="halRefHtml">&lt;i&gt;Inverse Problems&lt;/i&gt;, 2008, 24 (1), pp.1-18. &lt;a target="_blank" href="https://dx.doi.org/10.1088/0266-5611/24/1/015017"&gt;&amp;#x27E8;10.1088/0266-5611/24/1/015017&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Inverse Problems, 2008, 24 (1), pp.1-18. &amp;#x27E8;10.1088/0266-5611/24/1/015017&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno>
            <idno type="stamp" n="IECN">IECL - Institut Elie Cartan de Lorraine</idno>
            <idno type="stamp" n="INRIA-CHILE">INRIA Chile</idno>
            <idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</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="AM2I-UL">Pôle scientifique Automatique, Mathématiques, Informatique et leurs Intéractions de l'Université de Lorraine</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">Inverse problems for the Schrödinger equation via Carleman inequalities with degenerate weights</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Alberto</forename>
                    <surname>Mercado</surname>
                  </persName>
                  <email type="md5">e5804d0ec247e93c8a54aa3c4fc1d1ed</email>
                  <email type="domain">dim.uchile.cl</email>
                  <idno type="idhal" notation="numeric">848387</idno>
                  <idno type="halauthorid" notation="string">11172-848387</idno>
                  <affiliation ref="#struct-1812"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Axel</forename>
                    <surname>Osses</surname>
                  </persName>
                  <idno type="halauthorid">177185-0</idno>
                  <affiliation ref="#struct-40802"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Lionel</forename>
                    <surname>Rosier</surname>
                  </persName>
                  <email type="md5">c65833548ab0b6bf44700b3353efff83</email>
                  <email type="domain">univ-littoral.fr</email>
                  <idno type="idhal" notation="string">lionel-rosier</idno>
                  <idno type="idhal" notation="numeric">14724</idno>
                  <idno type="halauthorid" notation="string">2813-14724</idno>
                  <idno type="IDREF">https://www.idref.fr/081301146</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-5602-9799</idno>
                  <idno type="GOOGLE SCHOLAR">deLqIscAAAAJ&amp;hl=fr</idno>
                  <idno type="ISNI">http://isni.org/isni/0000000114928094</idno>
                  <idno type="VIAF">https://viaf.org/viaf/64894912</idno>
                  <affiliation ref="#struct-23"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">14847</idno>
                <idno type="issn">0266-5611</idno>
                <idno type="eissn">1361-6420</idno>
                <title level="j">Inverse Problems</title>
                <imprint>
                  <publisher>IOP Publishing</publisher>
                  <biblScope unit="volume">24</biblScope>
                  <biblScope unit="issue">1</biblScope>
                  <biblScope unit="pp">1-18</biblScope>
                  <date type="datePub">2008</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1088/0266-5611/24/1/015017</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="classification">35R30 ; 34A55 ; 35J10 ; 93B30 ; 93C20</classCode>
              <classCode scheme="halDomain" n="math.math-ap">Mathematics [math]/Analysis of PDEs [math.AP]</classCode>
              <classCode scheme="halDomain" n="math.math-oc">Mathematics [math]/Optimization and Control [math.OC]</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>Baudouin and Puel (2002 Inverse Problems 18 1537-54), investigated some inverse problems for the evolution Schr¨odinger equation bymeans of Carleman inequalities proved under a strict pseudoconvexity condition. We showhere that new Carleman inequalities for the Schr¨odinger equationmay be derived under a relaxed pseudoconvexity condition, which allows us to use degenerate weights with a spatial dependence of the type ψ(x) = x * e, where e is some fixed direction in RN. As a result, less restrictive boundary or internal observations are allowed to obtain the stability for the inverse problem consisting in retrieving a stationary potential in the Schr¨odinger equation from a single boundary or internal measurement.</p>
            </abstract>
            <particDesc>
              <org type="consortium">CORIDA</org>
            </particDesc>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-1812" status="VALID">
          <idno type="IdRef">164068007</idno>
          <idno type="ISNI">0000000122040669</idno>
          <idno type="RNSR">200419758N</idno>
          <idno type="ROR">https://ror.org/00wz2vk41</idno>
          <orgName>Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]</orgName>
          <orgName type="acronym">CMM</orgName>
          <date type="start">2000-01-01</date>
          <desc>
            <address>
              <addrLine>Av. Blanco Encalada 2120, Piso 7 2120 SANTIAGO DE CHILE</addrLine>
              <country key="CL"/>
            </address>
            <ref type="url">http://www.cmm.uchile.cl</ref>
          </desc>
          <listRelation>
            <relation active="#struct-142796" type="direct"/>
            <relation name="IRL2807 / UMI2807 / UMR2071" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-40802" status="VALID">
          <orgName>Departamento de Ingeniería Mecánica</orgName>
          <orgName type="acronym">DIMEC</orgName>
          <desc>
            <address>
              <addrLine>Beaucheff 850 5° Piso, SANTIAGO</addrLine>
              <country key="CL"/>
            </address>
            <ref type="url">http://www.dimec.uchile.cl/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-308666" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-23" status="OLD">
          <orgName>Institut Élie Cartan de Nancy</orgName>
          <orgName type="acronym">IECN</orgName>
          <date type="end">2012-12-31</date>
          <desc>
            <address>
              <addrLine>Université Henri Poincaré, Campus Scientifique, boulevard des Aiguillettes, 54000 Vandoeuvre-les-Nancy</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.iecn.u-nancy.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-300291" type="direct"/>
            <relation active="#struct-300292" type="direct"/>
            <relation active="#struct-300293" type="direct"/>
            <relation name="UMR7502 / UMR9973" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-142796" status="VALID">
          <idno type="ROR">https://ror.org/047gc3g35</idno>
          <orgName>Universidad de Chile = University of Chile [Santiago]</orgName>
          <orgName type="acronym">UCHILE</orgName>
          <desc>
            <address>
              <addrLine>Av. Libertador Bernardo O'Higgins 1058, Santiago de Chile</addrLine>
              <country key="CL"/>
            </address>
            <ref type="url">http://www.uchile.cl/</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="institution" xml:id="struct-308666" status="VALID">
          <idno type="IdRef">029256364</idno>
          <idno type="ROR">https://ror.org/02ma57s91</idno>
          <orgName>Universidad de Santiago de Chile [Santiago]</orgName>
          <orgName type="acronym">USACH</orgName>
          <date type="start">1981-03-21</date>
          <desc>
            <address>
              <addrLine>Universidad de Santiago de Chile. Avenida Libertador Bernardo O'Higgins nº 3363. Estación Central. Santiago. Chile</addrLine>
              <country key="CL"/>
            </address>
            <ref type="url">http://www.usach.cl/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300291" status="OLD">
          <orgName>Université Henri Poincaré - Nancy 1</orgName>
          <orgName type="acronym">UHP</orgName>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300292" status="OLD">
          <orgName>Université Nancy 2</orgName>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300293" status="OLD">
          <orgName>Institut National Polytechnique de Lorraine</orgName>
          <orgName type="acronym">INPL</orgName>
          <date type="end">2011-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>