Singular solutions for complex second order elliptic equations and their application to time-harmonic diffuse optical tomography

2024/04/03 by Curran, Jason, Gaburro, Romina, Nolan, Clifford · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.02987

Abstract

We construct singular solutions of a complex elliptic equation of second order, having an isolated singularity of any order. In particular, we extend results obtained for the real partial differential equation in divergence form by Alessandrini in 1990. Our solutions can be applied to the determination of the optical properties of an anisotropic medium in time-harmonic Diffuse Optical Tomography (DOT).

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• A uniqueness result in the inverse problem for the anisotropic Schrödinger type equation from local measurements

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