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Laplace Equation

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Theory and Applications of Partial Differential Equations

Part of the book series: Mathematical Concepts and Methods in Science and Engineering ((MCSENG,volume 46))

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Abstract

For a function u(x) = u(x 1,..., x n ) the differential equation

$$ \sum\limits_n^{i = 1} {{u_{{x_i}{x_i}}}} : = \Delta u = 0 $$
((L))

is called the Laplace equation (in ℝn). Its solutions are called harmonic functions.

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Authors and Affiliations

  1. University of Rome “La Sapienza”, Rome, Italy

    Piero Bassanini

  2. Wichita State University, Wichita, Kansas, USA

    Alan R. Elcrat

Authors
  1. Piero Bassanini
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  2. Alan R. Elcrat
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© 1997 Springer Science+Business Media New York

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Bassanini, P., Elcrat, A.R. (1997). Laplace Equation. In: Theory and Applications of Partial Differential Equations. Mathematical Concepts and Methods in Science and Engineering, vol 46. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1875-8_4

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  • DOI: https://doi.org/10.1007/978-1-4899-1875-8_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-1877-2

  • Online ISBN: 978-1-4899-1875-8

  • eBook Packages: Springer Book Archive

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