Fractional powers of sectorial operators via the Dirichlet-to-Neumann operator

2016/08/19 by W. Arendt, Wolfgang Arendt, A. F. M. ter Elst +5 · 4 citations
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #math.AP

paper · pdf · doi:10.48550/arxiv.1608.05707

arxiv created 2016/08/19 · openalex publication_date 2016/08/19 · arxiv updated 2016/08/22 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/01

Abstract

In the very influential paper \citeCS07 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 \citeST10 and Galé, Miana and Stinga \citeGMS13 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.

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