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

W. Arendt; A. F. M. ter Elst; M. Warma

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arXiv · 1608.05707

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

W. Arendt·A. F. M. ter Elst·M. Warma

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Abstract

In the very influential paper \cite{CS07} Caffarelli and Silvestre studied regularity of $(-\Delta)^s$, $0<s<1$, by identifying fractional powers with a certain Dirichlet-to-Neumann operator. Stinga and Torrea \cite{ST10} and Gal\'e, Miana and Stinga \cite{GMS13} 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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BibTeX RIS

W. Arendt, A. F. M. ter Elst, M. Warma. 2016-08-19. Fractional powers of sectorial operators via the Dirichlet-to-Neumann operator. https://arxiv.org/abs/1608.05707

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