Fractional powers of sectorial operators via the Dirichlet-to-Neumann operator
By Wolfgang Arendt, A. T. Elst, Mahamadi Warma. 2016
66 citations recorded by the source corpus.
ABSTRACT In the very influential paper [4] Caffarelli and Silvestre studied regularity of (−Δ)s, 0<s<1, by identifying fractional powers with a certain Dirichlet-to-Neumann operator. Stinga and Torrea [15] and Galé et al. [7] gave several more abstract versions of this extension procedure. The purpose of this paper is to study precise regularity properties of the Dirichlet and the Neumann problem in Hilbert spaces. Then the Dirichlet-to-Neumann operator becomes an isomorphism between interpolation spaces and its part in the underlying Hilbert space is exactly the fractional power.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/d2830089d2228fab141764faae718d7cd522decf
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In Applied Mathematics
In Computational Theory and Mathematics
In Mechanics of Materials
Citations in the corpus
- Boundary Value Problems, Weyl Functions, and Differential Operators (2020, background): “Furthermore, the recent contributions [35, 36, 37, 38, 39, 40] by Arendt, ter Elst, and coauthors form an interesting series of papers on elliptic differential operators and Dirichlet-to-Neumann operators based mainly on form methods.”