6533b839fe1ef96bd12a5a56
RESEARCH PRODUCT
Boundary reconstruction for the broken ray transform
Joonas Ilmavirtasubject
Mathematics - Differential GeometryDifferential Geometry (math.DG)GeodesicAstrophysics::High Energy Astrophysical PhenomenaGeneral MathematicsSecond fundamental formta111Mathematical analysisFOS: MathematicsBoundary (topology)Function (mathematics)53C65 78A05 (Primary) 35R30 58J32 (Secondary)Mathematicsdescription
We reduce boundary determination of an unknown function and its normal derivatives from the (possibly weighted and attenuated) broken ray data to the injectivity of certain geodesic ray transforms on the boundary. For determination of the values of the function itself we obtain the usual geodesic ray transform, but for derivatives this transform has to be weighted by powers of the second fundamental form. The problem studied here is related to Calder\'on's problem with partial data.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-10-08 | Annales Academiae Scientiarum Fennicae Mathematica |