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Laplace's equation

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English

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Alternative forms

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Noun

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Laplace's equation (plural Laplace's equations)

  1. (potential theory) The partial differential equation , commonly written or , where is the Laplace operator and is a scalar function.
    • 1993, V. V. Sarwate, Electromagnetic Fields and Waves, New Age International Publishers, page 182:
      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.
    • 1996, Peter P. Silvester, Ronald L. Ferrari, Finite elements for electrical engineers, 3rd edition, Cambridge University Press, page 29:
      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.
    • 2002, Gerald D. Mahan, Applied Mathematics, Kluwer Academic / Plenum, page 141,
      Laplace'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.

Usage notes

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The plural is rare in this form (and when used, often, although apparently not always, an error), but appears in the alternative form Laplace equations.

Further reading

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