Regularity of spectral fractional Dirichlet and Neumann problems

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Regularity of spectral fractional Dirichlet and Neumann problems. / Grubb, Gerd.

I: Mathematische Nachrichten, Bind 289, Nr. 7, 2016, s. 831–844.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Grubb, G 2016, 'Regularity of spectral fractional Dirichlet and Neumann problems', Mathematische Nachrichten, bind 289, nr. 7, s. 831–844. https://doi.org/10.1002/mana.201500041

APA

Grubb, G. (2016). Regularity of spectral fractional Dirichlet and Neumann problems. Mathematische Nachrichten, 289(7), 831–844. https://doi.org/10.1002/mana.201500041

Vancouver

Grubb G. Regularity of spectral fractional Dirichlet and Neumann problems. Mathematische Nachrichten. 2016;289(7):831–844. https://doi.org/10.1002/mana.201500041

Author

Grubb, Gerd. / Regularity of spectral fractional Dirichlet and Neumann problems. I: Mathematische Nachrichten. 2016 ; Bind 289, Nr. 7. s. 831–844.

Bibtex

@article{b5bebaeab51040eaa4a341d7108b1f9d,
title = "Regularity of spectral fractional Dirichlet and Neumann problems",
abstract = "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 H{\"o}lder 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.",
author = "Gerd Grubb",
year = "2016",
doi = "10.1002/mana.201500041",
language = "English",
volume = "289",
pages = "831–844",
journal = "Mathematische Nachrichten",
issn = "0025-584X",
publisher = "Wiley - V C H Verlag GmbH & Co. KGaA",
number = "7",

}

RIS

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