@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-WL1Z5XG9-5
  skos:prefLabel "opérateur hypoelliptique"@fr, "hypoelliptic operator"@en ;
  skos:definition """In the theory of partial differential equations, a partial differential operator <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle P}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>P</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle P}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="P"></span> defined on an open subset  
<br/>
<br/><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle U\\\\subset {\\\\mathbb {R} }^{n}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>U</mi>
<br/>        <mo>⊂<!-- ⊂ --></mo>
<br/>        <msup>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mrow class="MJX-TeXAtom-ORD">
<br/>              <mi mathvariant="double-struck">R</mi>
<br/>            </mrow>
<br/>          </mrow>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle U\\\\subset {\\\\mathbb {R} }^{n}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/893ddd4dd194d20fad830cbecb16abfc4978e0a7" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:7.778ex; height:2.343ex;" alt="{\\\\displaystyle U\\\\subset {\\\\mathbb {R} }^{n}}"></span></dd></dl>
<br/>is called <b>hypoelliptic</b> if for every distribution <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle u}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>u</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle u}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="u"></span> defined on an open subset  <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle V\\\\subset U}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>V</mi>
<br/>        <mo>⊂<!-- ⊂ --></mo>
<br/>        <mi>U</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle V\\\\subset U}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae37b0495b78ebcc4b8df66949ebd5659a4fafb6" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:6.668ex; height:2.176ex;" alt="{\\\\displaystyle V\\\\subset U}"></span> such that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle Pu}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>P</mi>
<br/>        <mi>u</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle Pu}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d08065b09683c0aef93775238fb51dd23d27d312" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:3.075ex; height:2.176ex;" alt="{\\\\displaystyle Pu}"></span> is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle C^{\\\\infty }}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mi>C</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle C^{\\\\infty }}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/971ed05871d69309df32efdfd2020128c9cf69d8" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:3.673ex; height:2.343ex;" alt="C^{\\\\infty }"></span> (smooth), <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle u}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>u</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle u}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="u"></span> must also be <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle C^{\\\\infty }}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mi>C</mi>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>          </mrow>
<br/>        </msup>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle C^{\\\\infty }}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/971ed05871d69309df32efdfd2020128c9cf69d8" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:3.673ex; height:2.343ex;" alt="C^{\\\\infty }"></span>.
<br/> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Hypoelliptic_operator">https://en.wikipedia.org/wiki/Hypoelliptic_operator</a>)"""@en ;
  skos:broader psr:-RRBN6FVB-9, psr:-LM732D0H-P ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Hypoelliptic_operator> ;
  dc:created "2023-08-04"^^xsd:date ;
  a skos:Concept ;
  dc:modified "2023-08-04"^^xsd:date ;
  skos:inScheme psr: .

psr:-RRBN6FVB-9
  skos:prefLabel "opérateur différentiel"@fr, "differential operator"@en ;
  a skos:Concept ;
  skos:narrower psr:-WL1Z5XG9-5 .

psr:-LM732D0H-P
  skos:prefLabel "équation aux dérivées partielles"@fr, "partial differential equation"@en ;
  a skos:Concept ;
  skos:narrower psr:-WL1Z5XG9-5 .