Ngô Quốc Anh

October 29, 2007

Dirichlet-to-Neumann operator

Filed under: Nghiên Cứu Khoa Học — Ngô Quốc Anh @ 23:29

You have a domain \Omega\subset \mathbb R^n and a partial differential equation (such as \Delta u=0) in that domain. Take a function \phi defined on \partial\Omega, solve the boundary value problem with u=\phi on the boundary, and compute \psi=\frac{\partial u}{\partial n}, the normal derivative of solution on the boundary. The map \phi\mapsto\psi is the D-n-N operator.

A typical problem (motivated by tomography) is to recover the PDE from the D-n-N operator.

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