Mathematisches Seminar

Prof. Dr. Wolfgang Arendt, Universität Ulm: "Fractional Powers via the Dirichlet to Neumann Operator"

15.12.2016 von 14:15 bis 15:30

LMS 4 - Raum 424 - Kleiner Hörsaal

Abstract:

We show that each sectorial operator A on Hilbert space leads to a well-posed Dirichlet-to-Neumann Problem with very precise regularity results.
This allows us to construct the fractional powers  of A in a definitely unusual way.
If A is the Laplacian such a construction was done before in a very influential paper by Caffarelli and Silvestre (without proving well posedness).


References:

W. Arendt, T. ter Elst, M. Warma: Fractional powers of sectorial operators via the Dirichlet-to-Neumann operator.
arXiv:1608.05707vl. 2016

L. Caffarelli, L. Silvestre: An extensions problem related to the fractional Laplacian. Comm. Partial Diff. Equ. 32 (2007) 1245-1260

 

Einladender: M. Haase

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