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Optimal principal eigenfunction for elliptic operators with large drift Rossi, Luca
Description
In a series of papers, F. Hamel, N. Nadirashvili and E. Russ deal with the isoperimetric problem for eigenvalues of second order elliptic operators. With respect to the classical Faber-Krahn inequality, they consider an additional drift term, which acts as a control under L infinity constraint. They solve the problem and derive the precise asymptotic of the principal eigenvalue as the norm of the drift tends to infinity. As a preliminary step, they consider the optimization problem in a fixed domain. This leads to a nonlinear eigenvalue problem. They conjecture that, in such case, the maximal points of the optimal principal eigenfunction approach the points with maximal distance from the boundary, and that its gradient aligns with the gradient of the distance function. We present a proof of the first conjecture and give a partial result concerning the second one. These results have been obtained in collaboration with F. Hamel and E. Russ.
Item Metadata
Title |
Optimal principal eigenfunction for elliptic operators with large drift
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-04-04T08:46
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Description |
In a series of papers, F. Hamel, N. Nadirashvili and E. Russ deal with the isoperimetric problem for eigenvalues of second order elliptic operators. With respect to the classical Faber-Krahn inequality, they consider an additional drift term, which acts as a control under L infinity constraint. They solve the problem and derive the precise asymptotic of the principal eigenvalue as the norm of the drift tends to infinity. As a preliminary step, they consider the optimization problem in a fixed domain. This leads to a nonlinear eigenvalue problem.
They conjecture that, in such case, the maximal points of the optimal principal eigenfunction approach the points with maximal distance from the boundary, and that its gradient aligns with the gradient of the distance function.
We present a proof of the first conjecture and give a partial result concerning the second one.
These results have been obtained in collaboration with F. Hamel and E. Russ.
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Extent |
51 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Ecoles Hautes Etudes en Sciences Sociales
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Series | |
Date Available |
2017-10-02
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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 |
10.14288/1.0355861
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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