Abstract
The Poisson equation \(\Delta u=f\) on a bounded open subset of \(\mathbb {R}^n\) is considered when f belongs to \(L_p(\Omega )\) for some p between 1 and 2 but does not belong to \(L_2(\Omega )\): The Hilbert space methods of earlier chapters are then not applicable, but use of a technique due to Simader and Sohr is shown to give a type of weak solution in the context of \(L_p\).
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Edmunds, D.E., Evans, W.D. (2018). The \(L_{p}\) Approach to 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_8
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DOI: https://doi.org/10.1007/978-3-030-02125-2_8
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Online ISBN: 978-3-030-02125-2
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