If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the ...
Brander, Tommi; Ilmavirta, Joonas; Piiroinen, Petteri; Tyni, Teemu(American Institute of Mathematical Sciences (AIMS), 2020)
We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam ...
We investigate a generalization of Calderón’s problem of recovering the conductivity coefficient in a conductivity equation from boundary measurements. As a model
equation we consider the p-conductivity equation
div σ ...
This note reviews certain classical applications of microlocal analysis in inverse problems. The text is based on lecture notes for a postgraduate level minicourse on applications of microlocal analysis in inverse problems, ...
Covi, Giovanni; Mönkkönen, Keijo; Railo, Jesse(American Institute of Mathematical Sciences (AIMS), 2021)
We prove a unique continuation property for the fractional Laplacian (−Δ)s when s∈(−n/2,∞)∖Z where n≥1. In addition, we study Poincaré-type inequalities for the operator (−Δ)s when s≥0. We apply the results to show that ...
