Non UBC
DSpace
Lauri Oksanen
2019-10-14T08:37:12Z
2019-04-16T10:33
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.
https://circle.library.ubc.ca/rest/handle/2429/71902?expand=metadata
40.0 minutes
video/mp4
Author affiliation: University College London
Banff (Alta.)
10.14288/1.0383384
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Researcher
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Global analysis, analysis on manifolds
Dynamical systems and ergodic theory
Global analysis
Inverse problem for a semi-linear elliptic equation
Moving Image
http://hdl.handle.net/2429/71902