"Laplace's equation" meaning in All languages combined

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        {
          "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"
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        {
          "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."
        }
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      "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."
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        "(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."
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          "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"
        },
        {
          "ref": "1996, Peter P. Silvester, Ronald L. Ferrari, Finite elements for electrical engineers, 3rd edition, Cambridge University Press, page 29:",
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          "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."
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      "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."
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  "word": "Laplace's equation"
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