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).
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© 1998 Springer-Verlag New York, Inc.
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(1998). Poisson’s Equation in Two Space Dimensions. In: Introduction to Partial Differential Equations. Texts in Applied Mathematics, vol 29. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22773-3_7
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DOI: https://doi.org/10.1007/978-0-387-22773-3_7
Publisher Name: Springer, New York, NY
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