Abstract
In this chapter, we describe and discuss differential potentials for the Laplace operator, their various interpretations and representations, and, particularly, their operator form resembling the one studied by Calderon [109] and Seeley [110] for general elliptic operators. Furthermore, we construct a difference potential for the difference analog of the Laplace operator and present a method for approximating a differential potential with a given density by a difference potential, which is relatively easy to calculate. We have used the term “differential” for potentials associated with differential operators so as to distinguish them from “difference” potentials corresponding to difference operators.
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© 2002 Springer-Verlag Berlin Heidelberg
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Ryaben’kii, V.S. (2002). Differential and Difference Potentials. In: Method of Difference Potentials and Its Applications. Springer Series in Computational Mathematics, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56344-7_3
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DOI: https://doi.org/10.1007/978-3-642-56344-7_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62715-6
Online ISBN: 978-3-642-56344-7
eBook Packages: Springer Book Archive