"Non UBC"@en .
"DSpace"@en .
"Lauri Oksanen"@en .
"2019-10-14T08:37:12Z"@en .
"2019-04-16T10:33"@en .
"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\nmanifold with boundary. We show that, under certain geometrical assumptions, the Dirichlet-to-Neumann map determines V for a large\nclass of non-linearities. The proof is constructive and is based on a multiple-fold linearization of the semi-linear equation near complex\ngeometric optics solutions for the linearized operator, and the resulting non-linear interactions. This approach allows us to reduce\nthe inverse problem boundary value problem to the purely geometric problem to invert a family of weighted ray transforms, that we call\nthe Jacobi weighted ray transform. This is a joint work with Ali Feizmohammadi."@en .
"https://circle.library.ubc.ca/rest/handle/2429/71902?expand=metadata"@en .
"40.0 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: University College London"@en .
"Banff (Alta.)"@en .
"10.14288/1.0383384"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivatives 4.0 International"@en .
"http://creativecommons.org/licenses/by-nc-nd/4.0/"@en .
"Researcher"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Global analysis, analysis on manifolds"@en .
"Dynamical systems and ergodic theory"@en .
"Global analysis"@en .
"Inverse problem for a semi-linear elliptic equation"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/71902"@en .