Regularity of spectral fractional Dirichlet and Neumann problems
Research output: Contribution to journal › Journal article › Research › peer-review
Consider the fractional powers and of the Dirichlet and Neumann realizations of a second-order strongly elliptic differential operator A on a smooth bounded subset Ω of .
Recalling the results on complex powers and complex interpolation of
domains of elliptic boundary value problems by Seeley in the 1970's, we
demonstrate how they imply regularity properties in full scales of -Sobolev
spaces and Hölder spaces, for the solutions of the associated
equations. Extensions to nonsmooth situations for low values of s are derived by use of recent results on -calculus.
We also include an overview of the various Dirichlet- and Neumann-type
boundary problems associated with the fractional Laplacian.
Original language | English |
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Journal | Mathematische Nachrichten |
Volume | 289 |
Issue number | 7 |
Pages (from-to) | 831–844 |
ISSN | 0025-584X |
DOIs | |
Publication status | Published - 2016 |
ID: 148728415