6533b7dafe1ef96bd126d8e4
RESEARCH PRODUCT
Partial Data Problems and Unique Continuation in Scalar and Vector Field Tomography
Joonas IlmavirtaKeijo Mönkkönensubject
osittaisdifferentiaaliyhtälötvector field tomographyinverse problemstomografiaApplied MathematicsGeneral MathematicsX-ray tomographyregion of interest tomographyunique continuationinversio-ongelmatAnalysisdescription
AbstractWe 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-03-26 | Journal of Fourier Analysis and Applications |