6533b7d6fe1ef96bd126726d

RESEARCH PRODUCT

Partial data inverse problems for the Hodge Laplacian

Leo TzouMikko SaloFrancis J. Chung

subject

Mathematics - Differential GeometryPure mathematicsadmissible manifoldsType (model theory)partial data01 natural sciences58J32inversio-ongelmatMathematics - Analysis of PDEsFOS: MathematicsBoundary value problemUniquenessTensor0101 mathematicsMathematicsNumerical Analysisabsolute and relative boundary conditionsGeometrical opticsinverse problemsApplied Mathematicsta111010102 general mathematicsScalar (physics)Inverse problemCarleman estimates010101 applied mathematics35R30Differential Geometry (math.DG)Hodge LaplacianLaplace operatorAnalysisAnalysis of PDEs (math.AP)

description

We prove uniqueness results for a Calderon type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or absolute-to-relative boundary value maps uniquely determine a zeroth order potential. The method is based on Carleman estimates for the Hodge Laplacian with relative or absolute boundary conditions, and on the construction of complex geometric optics solutions which reduce the Calderon type problem to a tensor tomography problem for 2-tensors. The arguments in this paper allow to establish partial data results for elliptic systems that generalize the scalar results due to Kenig-Sjostrand-Uhlmann.

yearjournalcountryeditionlanguage
2017-01-01Analysis & PDE
https://doi.org/10.2140/apde.2017.10.43