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Symmetry results in the half space for a semi-linear fractional Laplace equation\\ through a one-dimensional analysis Quaas, Alexander
Description
In this talk we analyze the semi-linear fractional Laplace equation $$(-\Delta)^s u = f(u) \quad\text{ in } \mathbb{R}^N_+,\quad u=0 \quad\text{ in } \mathbb{R}^N\setminus \mathbb{R}^N_+,$$ where $\R^N_+=\{x=(x',x_N)\in \R^N:\ x_N>0\}$ stands for the half-space and $f$ is a locally Lipschitz nonlinearity. We completely characterize one-dimensional bounded solutions of this problem, and we prove among other things that if $u$ is a bounded solution with $\rho:=\sup_{\mathbb{R}^N}u$ verifying $f(\rho)=0$, then $u$ is necessarily one-dimensional.
Item Metadata
Title |
Symmetry results in the half space for a semi-linear fractional Laplace equation\\ through a one-dimensional analysis
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-04-06T11:31
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Description |
In this talk we analyze the semi-linear fractional Laplace equation
$$(-\Delta)^s u = f(u) \quad\text{ in } \mathbb{R}^N_+,\quad u=0 \quad\text{ in } \mathbb{R}^N\setminus \mathbb{R}^N_+,$$
where $\R^N_+=\{x=(x',x_N)\in \R^N:\ x_N>0\}$ stands for the half-space and $f$ is a locally
Lipschitz nonlinearity. We completely characterize one-dimensional bounded solutions of this problem, and we prove
among other things that if $u$ is a bounded solution with $\rho:=\sup_{\mathbb{R}^N}u$ verifying $f(\rho)=0$, then $u$ is
necessarily one-dimensional.
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Extent |
37 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Valparaiso (Chile)
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Series | |
Date Available |
2017-10-04
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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 |
10.14288/1.0356061
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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 Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International