Fractional-order operators: Boundary problems, heat equations
Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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.
Originalsprog | Engelsk |
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Titel | Mathematical Analysis and Applications-Plenary Lectures - ISAAC 2017 |
Redaktører | Joachim Toft, Luigi G. Rodino |
Antal sider | 31 |
Forlag | Springer |
Publikationsdato | 2018 |
Sider | 51-81 |
ISBN (Trykt) | 9783030008734 |
DOI | |
Status | Udgivet - 2018 |
Begivenhed | 11th International Society for Analysis, its Applications and Computation, ISAAC 2017 - Vaxjo, Sverige Varighed: 14 aug. 2017 → 18 aug. 2017 |
Konference
Konference | 11th International Society for Analysis, its Applications and Computation, ISAAC 2017 |
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Land | Sverige |
By | Vaxjo |
Periode | 14/08/2017 → 18/08/2017 |
Navn | Springer Proceedings in Mathematics & Statistics |
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Vol/bind | 262 |
ISSN | 2194-1009 |
ID: 214023447