"elliptic operator" meaning in All languages combined

{
  "etymology_text": "From its association with a corresponding elliptic partial differential equation — a second-order linear partial differential equation with coefficients specified analogously to those of the equation of a conic section that generates an ellipse.",
  "forms": [
    {
      "form": "elliptic operators",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "elliptic operator (plural elliptic operators)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "coordinate_terms": [
        {
          "word": "hyperbolic operator"
        },
        {
          "word": "parabolic operator"
        }
      ],
      "examples": [
        {
          "text": "2001, L. Gross, Heat Kernel Analysis on Lie Groups, Laurent Decreusefond, Bernt Øksendal, Ali S. Üstünel (editors), Stochastic Analysis and Related Topics VII: Proceedings of the Seventh Silivri Workshop, Springer-Verlag (Birkhäuser), page 1,\nThe study of second order elliptic operators over some of these infinite dimensional manifolds has been the subject of much work in the past forty years, some of it for the purposes of quantum field theory and some of it for the purposes of stochastic analysis or infinite dimensional differential topology."
        },
        {
          "ref": "2008, Vladimir E. Nazaikinskii, Anton Yu. Savin, Boris Yu. Sternin, Elliptic Theory and Noncommutative Geometry: Nonlocal Elliptic Operators, Springer, page 37:",
          "text": "Just as in the usual elliptic theory, in the theory of nonlocal elliptic operators we need not restrict ourselves to individual operators but can also consider families of nonlocal elliptic operators.",
          "type": "quote"
        },
        {
          "ref": "2014, Lester L. Helms, Potential Theory, 2nd edition, Springer, page 412:",
          "text": "The Dirichlet problem for an elliptic operator was solved in Chap. 10 by morphing a solution of the Dirichlet problem for the Laplacian on a ball into a solution of the Dirichlet problem for an elliptic operator on a ball.",
          "type": "quote"
        }
      ],
      "glosses": [
        "Any of a particular class of second-order linear differential operators."
      ],
      "hyponyms": [
        {
          "sense": "second-order linear differential operator",
          "word": "Laplace operator"
        }
      ],
      "id": "en-elliptic_operator-en-noun-CRZYEHbk",
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "differential operator",
          "differential operator"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) Any of a particular class of second-order linear differential operators."
      ],
      "related": [
        {
          "word": "hypoelliptic operator"
        }
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "elliptic partial differential equation"
      ]
    }
  ],
  "word": "elliptic operator"
}

{
  "coordinate_terms": [
    {
      "word": "hyperbolic operator"
    },
    {
      "word": "parabolic operator"
    }
  ],
  "etymology_text": "From its association with a corresponding elliptic partial differential equation — a second-order linear partial differential equation with coefficients specified analogously to those of the equation of a conic section that generates an ellipse.",
  "forms": [
    {
      "form": "elliptic operators",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "elliptic operator (plural elliptic operators)",
      "name": "en-noun"
    }
  ],
  "hyponyms": [
    {
      "sense": "second-order linear differential operator",
      "word": "Laplace operator"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "hypoelliptic operator"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Mathematical analysis"
      ],
      "examples": [
        {
          "text": "2001, L. Gross, Heat Kernel Analysis on Lie Groups, Laurent Decreusefond, Bernt Øksendal, Ali S. Üstünel (editors), Stochastic Analysis and Related Topics VII: Proceedings of the Seventh Silivri Workshop, Springer-Verlag (Birkhäuser), page 1,\nThe study of second order elliptic operators over some of these infinite dimensional manifolds has been the subject of much work in the past forty years, some of it for the purposes of quantum field theory and some of it for the purposes of stochastic analysis or infinite dimensional differential topology."
        },
        {
          "ref": "2008, Vladimir E. Nazaikinskii, Anton Yu. Savin, Boris Yu. Sternin, Elliptic Theory and Noncommutative Geometry: Nonlocal Elliptic Operators, Springer, page 37:",
          "text": "Just as in the usual elliptic theory, in the theory of nonlocal elliptic operators we need not restrict ourselves to individual operators but can also consider families of nonlocal elliptic operators.",
          "type": "quote"
        },
        {
          "ref": "2014, Lester L. Helms, Potential Theory, 2nd edition, Springer, page 412:",
          "text": "The Dirichlet problem for an elliptic operator was solved in Chap. 10 by morphing a solution of the Dirichlet problem for the Laplacian on a ball into a solution of the Dirichlet problem for an elliptic operator on a ball.",
          "type": "quote"
        }
      ],
      "glosses": [
        "Any of a particular class of second-order linear differential operators."
      ],
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "differential operator",
          "differential operator"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) Any of a particular class of second-order linear differential operators."
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "elliptic partial differential equation"
      ]
    }
  ],
  "word": "elliptic operator"
}