"Laplace's equation" meaning in English

{
  "forms": [
    {
      "form": "Laplace's equations",
      "tags": [
        "plural"
      ]
    },
    {
      "form": "Laplace equation",
      "tags": [
        "alternative"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Laplace's equation (plural Laplace's equations)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Bulgarian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "langcode": "en",
          "name": "Differential equations",
          "orig": "en:Differential equations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "langcode": "en",
          "name": "Potential theory",
          "orig": "en:Potential theory",
          "parents": [],
          "source": "w"
        }
      ],
      "examples": [
        {
          "bold_text_offsets": [
            [
              136,
              154
            ]
          ],
          "ref": "1993, V. V. Sarwate, Electromagnetic Fields and Waves, New Age International Publishers, page 182:",
          "text": "In practical problems, since the charges are confined to small regions while major part of the space is charge-free, it is obvious that Laplace's Equation has far greater utility than Poisson's equation.",
          "type": "quote"
        },
        {
          "bold_text_offsets": [
            [
              66,
              84
            ],
            [
              158,
              176
            ]
          ],
          "ref": "1996, Peter P. Silvester, Ronald L. Ferrari, Finite elements for electrical engineers, 3rd edition, Cambridge University Press, page 29:",
          "text": "Numerous problems in electrical engineering require a solution of Laplace's equation in two dimensions. This section outlines a classic problem that leads to Laplace's equation, then develops a finite element method for its solution.",
          "type": "quote"
        },
        {
          "text": "2002, Gerald D. Mahan, Applied Mathematics, Kluwer Academic / Plenum, page 141,\nLaplace's equation appears in a variety of physics problems and several examples are provided below. The relevance of Laplace's equation to complex variables is provided by the following important theorem."
        }
      ],
      "glosses": [
        "The partial differential equation (∂²φ)/(∂x_1²)+(∂²φ)/(∂x_2²)+⋯+(∂²φ)/(∂x_n²)=0, commonly written Δφ=0 or ∇²φ=0, where Δ(=∇²) is the Laplace operator and φ is a scalar function."
      ],
      "id": "en-Laplace's_equation-en-noun-Y0U~m7Z~",
      "links": [
        [
          "potential theory",
          "potential theory"
        ],
        [
          "partial differential equation",
          "partial differential equation"
        ],
        [
          "Laplace operator",
          "Laplace operator"
        ],
        [
          "scalar function",
          "scalar function"
        ]
      ],
      "qualifier": "potential theory",
      "raw_glosses": [
        "(potential theory) The partial differential equation (∂²φ)/(∂x_1²)+(∂²φ)/(∂x_2²)+⋯+(∂²φ)/(∂x_n²)=0, commonly written Δφ=0 or ∇²φ=0, where Δ(=∇²) is the Laplace operator and φ is a scalar function."
      ],
      "translations": [
        {
          "code": "bg",
          "lang": "Bulgarian",
          "roman": "uravnenie na Laplas",
          "sense": "PDE",
          "tags": [
            "neuter"
          ],
          "word": "уравнение на Лаплас"
        }
      ],
      "wikipedia": [
        "Laplace's equation"
      ]
    }
  ],
  "word": "Laplace's equation"
}

{
  "forms": [
    {
      "form": "Laplace's equations",
      "tags": [
        "plural"
      ]
    },
    {
      "form": "Laplace equation",
      "tags": [
        "alternative"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Laplace's equation (plural Laplace's equations)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with Bulgarian translations",
        "en:Differential equations",
        "en:Potential theory"
      ],
      "examples": [
        {
          "bold_text_offsets": [
            [
              136,
              154
            ]
          ],
          "ref": "1993, V. V. Sarwate, Electromagnetic Fields and Waves, New Age International Publishers, page 182:",
          "text": "In practical problems, since the charges are confined to small regions while major part of the space is charge-free, it is obvious that Laplace's Equation has far greater utility than Poisson's equation.",
          "type": "quote"
        },
        {
          "bold_text_offsets": [
            [
              66,
              84
            ],
            [
              158,
              176
            ]
          ],
          "ref": "1996, Peter P. Silvester, Ronald L. Ferrari, Finite elements for electrical engineers, 3rd edition, Cambridge University Press, page 29:",
          "text": "Numerous problems in electrical engineering require a solution of Laplace's equation in two dimensions. This section outlines a classic problem that leads to Laplace's equation, then develops a finite element method for its solution.",
          "type": "quote"
        },
        {
          "text": "2002, Gerald D. Mahan, Applied Mathematics, Kluwer Academic / Plenum, page 141,\nLaplace's equation appears in a variety of physics problems and several examples are provided below. The relevance of Laplace's equation to complex variables is provided by the following important theorem."
        }
      ],
      "glosses": [
        "The partial differential equation (∂²φ)/(∂x_1²)+(∂²φ)/(∂x_2²)+⋯+(∂²φ)/(∂x_n²)=0, commonly written Δφ=0 or ∇²φ=0, where Δ(=∇²) is the Laplace operator and φ is a scalar function."
      ],
      "links": [
        [
          "potential theory",
          "potential theory"
        ],
        [
          "partial differential equation",
          "partial differential equation"
        ],
        [
          "Laplace operator",
          "Laplace operator"
        ],
        [
          "scalar function",
          "scalar function"
        ]
      ],
      "qualifier": "potential theory",
      "raw_glosses": [
        "(potential theory) The partial differential equation (∂²φ)/(∂x_1²)+(∂²φ)/(∂x_2²)+⋯+(∂²φ)/(∂x_n²)=0, commonly written Δφ=0 or ∇²φ=0, where Δ(=∇²) is the Laplace operator and φ is a scalar function."
      ],
      "wikipedia": [
        "Laplace's equation"
      ]
    }
  ],
  "translations": [
    {
      "code": "bg",
      "lang": "Bulgarian",
      "roman": "uravnenie na Laplas",
      "sense": "PDE",
      "tags": [
        "neuter"
      ],
      "word": "уравнение на Лаплас"
    }
  ],
  "word": "Laplace's equation"
}