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Inverse problem for a semi-linear elliptic equation Oksanen, Lauri
Description
We consider the Dirichlet-to-Neumann map, defined in a suitable sense, for the equation $-\Delta u + V(x,u)=0$ on a compact Riemannian manifold with boundary. We show that, under certain geometrical assumptions, the Dirichlet-to-Neumann map determines V for a large class of non-linearities. The proof is constructive and is based on a multiple-fold linearization of the semi-linear equation near complex geometric optics solutions for the linearized operator, and the resulting non-linear interactions. This approach allows us to reduce the inverse problem boundary value problem to the purely geometric problem to invert a family of weighted ray transforms, that we call the Jacobi weighted ray transform. This is a joint work with Ali Feizmohammadi.
Item Metadata
Title |
Inverse problem for a semi-linear elliptic equation
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2019-04-16T10:33
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Description |
We consider the Dirichlet-to-Neumann map, defined in a suitable sense, for the equation $-\Delta u + V(x,u)=0$ on a compact Riemannian
manifold with boundary. We show that, under certain geometrical assumptions, the Dirichlet-to-Neumann map determines V for a large
class of non-linearities. The proof is constructive and is based on a multiple-fold linearization of the semi-linear equation near complex
geometric optics solutions for the linearized operator, and the resulting non-linear interactions. This approach allows us to reduce
the inverse problem boundary value problem to the purely geometric problem to invert a family of weighted ray transforms, that we call
the Jacobi weighted ray transform. This is a joint work with Ali Feizmohammadi.
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Extent |
40.0 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 College London
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Series | |
Date Available |
2019-10-14
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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 |
10.14288/1.0383384
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Researcher
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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