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Gerd Grubb - Microlocal and Global Analysis, In...

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Gerd Grubb - Microlocal and Global Analysis, Interactions with Geometry

Fractional-order operators and transmission spaces.

For a strongly elliptic pseudodi erential operator P of order 2a (generally noninteger) | for example
the fractional Laplacian (􀀀)a, 0 < a < 1 | there is a useful theory for boundary value problems on smooth subsets

of Rn, when P satis es Hormander's a-transmission condition at the boundary. For the homogeneous Dirichlet
problem (u supported in
), the solution space for data in Hs(
), s  0, is then the a-transmission space
) = (􀀀a)
+ e+Ha+s(
), where (t)
+ denotes an order-reducing pseudodi erential operator of plus-type. A
similar result holds in Holder-Zygmund spaces. We shall give a more down-to-earth description of the transmission
spaces, involving a power da of the distance d(x) = dist(x; @
) and a Poisson solution operator for the Laplacian.
There are nice

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Hinzugefügt am: 10 Sep 2019
Mehr in: Öffentlich - Mathematik
Dauer: 00:40:22

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