The Laplace Equation

  • Sandro Salsa
Part of the Universitext book series (UTX)


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.


Harmonic Function Green Function Dirichlet Problem Fundamental Solution Laplace Equation 
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Copyright information

© Springer-Verlag Italia 2008

Authors and Affiliations

  • Sandro Salsa
    • 1
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoItaly

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