Abstract
The Laplace equation Δu = 0 occurs frequently in 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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© 2008 Springer-Verlag Italia
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Salsa, S. (2008). The Laplace Equation. In: Partial Differential Equations in Action. Universitext. Springer, Milano. https://doi.org/10.1007/978-88-470-0752-9_3
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DOI: https://doi.org/10.1007/978-88-470-0752-9_3
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-0751-2
Online ISBN: 978-88-470-0752-9
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