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Fractional Laplacian of divergent functions Valdinoci, Enrico
Description
We introduce a notion of fractional Laplacian for functions which grow more than linearly at infinity. In such case, the operator is not defined in the classical sense: nevertheless, we can give an ad-hoc definition which can be useful for applications in various fields, such as blowup and free boundary problems. In this setting, when the solution has a polynomial growth at infinity, the right hand side of the equation is not just a function, but an equivalence class of functions modulo polynomials of a fixed order. We also present a sharp version of the Schauder estimates in this framework and a Liouville Theorem. The results presented have been recently obtained in collaboration with Serena Dipierro and Ovidiu Savin.
Item Metadata
Title |
Fractional Laplacian of divergent functions
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-09-28T15:45
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Description |
We introduce a notion of fractional Laplacian
for functions which grow more than linearly at infinity. In such case,
the operator is not defined in the classical sense: nevertheless,
we can give an ad-hoc definition which can be
useful for applications in various fields,
such as blowup and free boundary problems.
In this setting, when the solution has a polynomial
growth at infinity, the right hand side of the equation
is not just a function, but an equivalence class of functions
modulo polynomials of a fixed order.
We also present a sharp version of the Schauder estimates in this framework and a Liouville Theorem.
The results presented have been recently obtained in collaboration
with Serena Dipierro and Ovidiu Savin.
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Extent |
49 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Melbourne
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Series | |
Date Available |
2017-03-30
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0343406
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International