Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

The Calderón problem is an inverse source problem (1511.01700v1)

Published 5 Nov 2015 in math.AP

Abstract: We prove that uniqueness for the Calder\'on problem on a Riemannian manifold with boundary follows from a hypothetical unique continuation property for the elliptic operator $\Delta+V+(\Lambda{1}_{t}-q)\otimes (\Lambda{2}_{t}-q)$ defined on $\partial\mathcal{M}{2}\times [0,1]$ where $V$ and $q$ are potentials and $\Lambda{i}_{t}$ is a Dirichlet-Neumann operator at depth $t$. This is done by showing that the difference of two Dirichlet-Neumann maps is equal to the Neumann boundary values of the solution to an inhomogeneous equation for said operator, where the source term is a measure supported on the diagonal of $\partial\mathcal{M}{2}$.

Summary

We haven't generated a summary for this paper yet.