Abstract
The fundamental properties of harmonic and subharmonic functions are given together with maximum principles, the representation of solutions of the Poisson equation, Weyl’s lemma and Perron’s method for proving existence of solutions of the Dirichlet problem.
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Edmunds, D.E., Evans, W.D. (2018). The Laplace Operator. In: Elliptic Differential Operators and Spectral Analysis. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-02125-2_2
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DOI: https://doi.org/10.1007/978-3-030-02125-2_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-02124-5
Online ISBN: 978-3-030-02125-2
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