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Concentrating solutions for a Hénon-type problem on general domains Faya, Jorge
Description
We consider the problem% \begin{equation*} \qquad\left\{ \begin{array} [c]{ll}% -\Delta u = \beta(x)|u|^{p-1-\epsilon }u & \text{in }\Omega,\\ u=0 & \text{on }\partial\Omega, \end{array} \right. \end{equation*} where $\Omega$ is a bounded smooth domain in $\mathbb{R}^{N}$, $N\geq3,$ $p:=\frac{N+2}{N-2}$ is the Sobolev critical exponent, $\epsilon$ is a small positive parameter and the function $\beta\in C^{1}(\overline{\Omega})$ is strictly positive on $\overline{\Omega}$. In this talk we shall present a recent result about the existence of positive and sign changing solutions whose asymptotic profile is a sum of $k$ bubbles which accumulate at a single point at the boundary as $\varepsilon$ tends to zero. This is joint work with professors Juan D\'avila and Fethi Mahmoudi.
Item Metadata
Title |
Concentrating solutions for a Hénon-type problem on general domains
|
Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
Date Issued |
2016-09-27T11:45
|
Description |
We consider the problem%
\begin{equation*}
\qquad\left\{
\begin{array}
[c]{ll}%
-\Delta u = \beta(x)|u|^{p-1-\epsilon }u & \text{in }\Omega,\\
u=0 & \text{on }\partial\Omega,
\end{array}
\right.
\end{equation*}
where $\Omega$ is a bounded smooth domain in $\mathbb{R}^{N}$, $N\geq3,$ $p:=\frac{N+2}{N-2}$ is the Sobolev critical exponent, $\epsilon$ is a small positive parameter and the function $\beta\in C^{1}(\overline{\Omega})$ is strictly positive on $\overline{\Omega}$.
In this talk we shall present a recent result about the existence of positive and sign changing solutions whose asymptotic profile is a sum of $k$ bubbles which accumulate at a single point at the boundary as $\varepsilon$ tends to zero.
This is joint work with professors Juan D\'avila and Fethi Mahmoudi.
|
Extent |
30 minutes
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Subject | |
Type | |
File Format |
video/mp4
|
Language |
eng
|
Notes |
Author affiliation: Universidad de Chile
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Series | |
Date Available |
2017-03-29
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0343384
|
URI | |
Affiliation | |
Peer Review Status |
Unreviewed
|
Scholarly Level |
Postdoctoral
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International