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Poisson’s Equation in Two Space Dimensions

Part of the Texts in Applied Mathematics book series (TAM, volume 29)

Abstract

Poisson’s equation is a fundamental partial differential equation which arises in many areas of mathematical physics, for example in fluid flow, flow in porous media, and electrostatics. We have already encountered this equation in Section 6.4 above, where we studied the maximum principle for harmonic functions. As a corollary of the maximum principle we have in fact already established that the Dirichlet problem for Poisson’s equation has at most one solution (see Theorem 6.8).

Keywords

Harmonic Function Maximum Principle Space Dimension Gaussian Elimination Divergence Theorem 
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Copyright information

© Springer-Verlag New York, Inc. 1998

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