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Title	Inverse problem for a semi-linear elliptic equation
Creator	Lauri Oksanen
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2019-04-16T10:33
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.
Extent	40.0 minutes
Subject	Mathematics Global analysis, analysis on manifolds Dynamical systems and ergodic theory Global analysis
Geographic Location	Banff (Alta.)
Type	Moving Image
FileFormat	video/mp4
Language	eng
Notes	Author affiliation: University College London
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2019-10-14
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0383384
URI	http://hdl.handle.net/2429/71902
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Researcher
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
AggregatedSourceRepository	DSpace

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