Abstract
The Laplace equation Δu = 0 occurs frequently in the applied sciences, in particular in the study of the steady state phenomena. Its solutions are called harmonic functions. For instance, the equilibrium position of a perfectly elastic membrane is a harmonic function as it is the velocity potential of a homogeneous fluid. Also, the steady state temperature of a homogeneous and isotropic body is a harmonic function and in this case Laplace equation constitutes the stationary counterpart (time independent) of the diffusion equation.
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© 2016 Springer International Publishing Switzerland
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Salsa, S. (2016). The Laplace Equation. In: Partial Differential Equations in Action. UNITEXT(), vol 99. Springer, Cham. https://doi.org/10.1007/978-3-319-31238-5_3
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DOI: https://doi.org/10.1007/978-3-319-31238-5_3
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-31237-8
Online ISBN: 978-3-319-31238-5
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