Regularity of spectral fractional Dirichlet and Neumann problems
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Regularity of spectral fractional Dirichlet and Neumann problems. / Grubb, Gerd.
In: Mathematische Nachrichten, Vol. 289, No. 7, 2016, p. 831–844.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Regularity of spectral fractional Dirichlet and Neumann problems
AU - Grubb, Gerd
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
U2 - 10.1002/mana.201500041
DO - 10.1002/mana.201500041
M3 - Journal article
VL - 289
SP - 831
EP - 844
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
IS - 7
ER -
ID: 148728415