Fractional-order operators: Boundary problems, heat equations

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt

Standard

Fractional-order operators : Boundary problems, heat equations. / Grubb, Gerd.

Mathematical Analysis and Applications-Plenary Lectures - ISAAC 2017. red. / Joachim Toft; Luigi G. Rodino. Springer, 2018. s. 51-81 (Springer Proceedings in Mathematics & Statistics, Bind 262).

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt

Harvard

Grubb, G 2018, Fractional-order operators: Boundary problems, heat equations. i J Toft & LG Rodino (red), Mathematical Analysis and Applications-Plenary Lectures - ISAAC 2017. Springer, Springer Proceedings in Mathematics & Statistics, bind 262, s. 51-81, 11th International Society for Analysis, its Applications and Computation, ISAAC 2017, Vaxjo, Sverige, 14/08/2017. https://doi.org/10.1007/978-3-030-00874-1_2

APA

Grubb, G. (2018). Fractional-order operators: Boundary problems, heat equations. I J. Toft, & L. G. Rodino (red.), Mathematical Analysis and Applications-Plenary Lectures - ISAAC 2017 (s. 51-81). Springer. Springer Proceedings in Mathematics & Statistics Bind 262 https://doi.org/10.1007/978-3-030-00874-1_2

Vancouver

Grubb G. Fractional-order operators: Boundary problems, heat equations. I Toft J, Rodino LG, red., Mathematical Analysis and Applications-Plenary Lectures - ISAAC 2017. Springer. 2018. s. 51-81. (Springer Proceedings in Mathematics & Statistics, Bind 262). https://doi.org/10.1007/978-3-030-00874-1_2

Author

Grubb, Gerd. / Fractional-order operators : Boundary problems, heat equations. Mathematical Analysis and Applications-Plenary Lectures - ISAAC 2017. red. / Joachim Toft ; Luigi G. Rodino. Springer, 2018. s. 51-81 (Springer Proceedings in Mathematics & Statistics, Bind 262).

Bibtex

@inproceedings{27d482ebd8ac4e1d9af5b21dc03cfea9,
title = "Fractional-order operators: Boundary problems, heat equations",
abstract = "The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on Lp-estimates up to the boundary, as well as recent H{\"o}lder estimates. This is supplied with new higher regularity estimates in L2 -spaces using a technique of Lions and Magenes, and higher Lp-regularity estimates (with arbitrarily high H{\"o}lder estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial C∞-regularity at the boundary is not in general possible.",
keywords = "Dirichlet and Neumann conditions, Fractional Laplacian, Green{\textquoteright}s formula, Heat equation, Pseudodifferential operator, Space-time regularity, Stable process",
author = "Gerd Grubb",
year = "2018",
doi = "10.1007/978-3-030-00874-1_2",
language = "English",
isbn = "9783030008734",
series = "Springer Proceedings in Mathematics & Statistics",
publisher = "Springer",
pages = "51--81",
editor = "Joachim Toft and Rodino, {Luigi G.}",
booktitle = "Mathematical Analysis and Applications-Plenary Lectures - ISAAC 2017",
address = "Switzerland",
note = "11th International Society for Analysis, its Applications and Computation, ISAAC 2017 ; Conference date: 14-08-2017 Through 18-08-2017",

}

RIS

TY - GEN

T1 - Fractional-order operators

T2 - 11th International Society for Analysis, its Applications and Computation, ISAAC 2017

AU - Grubb, Gerd

PY - 2018

Y1 - 2018

N2 - The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on Lp-estimates up to the boundary, as well as recent Hölder estimates. This is supplied with new higher regularity estimates in L2 -spaces using a technique of Lions and Magenes, and higher Lp-regularity estimates (with arbitrarily high Hölder estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial C∞-regularity at the boundary is not in general possible.

AB - The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on Lp-estimates up to the boundary, as well as recent Hölder estimates. This is supplied with new higher regularity estimates in L2 -spaces using a technique of Lions and Magenes, and higher Lp-regularity estimates (with arbitrarily high Hölder estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial C∞-regularity at the boundary is not in general possible.

KW - Dirichlet and Neumann conditions

KW - Fractional Laplacian

KW - Green’s formula

KW - Heat equation

KW - Pseudodifferential operator

KW - Space-time regularity

KW - Stable process

UR - http://www.scopus.com/inward/record.url?scp=85056909386&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-00874-1_2

DO - 10.1007/978-3-030-00874-1_2

M3 - Article in proceedings

AN - SCOPUS:85056909386

SN - 9783030008734

T3 - Springer Proceedings in Mathematics & Statistics

SP - 51

EP - 81

BT - Mathematical Analysis and Applications-Plenary Lectures - ISAAC 2017

A2 - Toft, Joachim

A2 - Rodino, Luigi G.

PB - Springer

Y2 - 14 August 2017 through 18 August 2017

ER -

ID: 214023447