Partial Data Problems and Unique Continuation in Scalar and Vector Field Tomography
Ilmavirta, J., & Mönkkönen, K. (2022). Partial Data Problems and Unique Continuation in Scalar and Vector Field Tomography. Journal of Fourier Analysis and Applications, 28(2), Article 34. https://doi.org/10.1007/s00041-022-09907-9
Published inJournal of Fourier Analysis and Applications
DisciplineMatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse Problems
© 2022 the Authors
We prove that if P(D) is some constant coefficient partial differential operator and f is a scalar field such that P(D)f vanishes in a given open set, then the integrals of f over all lines intersecting that open set determine the scalar field uniquely everywhere. This is done by proving a unique continuation property of fractional Laplacians which implies uniqueness for the partial data problem. We also apply our results to partial data problems of vector fields.
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Related funder(s)Academy of Finland
Funding program(s)Centre of Excellence, AoF; Academy Project, AoF
Additional information about fundingJ.I. was supported by Academy of Finland (grants 332890 and 336254). K.M. was supported by Academy of Finland (Centre of Excellence in Inverse Modelling and Imaging, grant numbers 284715 and 309963). Open Access funding provided by University of Jyväskylä (JYU).
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