Partial data inverse problems for the Hodge Laplacian
Chung, F. J., Salo, M., & Tzou, L. (2017). Partial data inverse problems for the Hodge Laplacian. Analysis and PDE, 10(1), 43-93. https://doi.org/10.2140/apde.2017.10.43
Published inAnalysis and PDE
© the Authors, 2017. Published in this repository with the kind permission of the publisher.
We prove uniqueness results for a Calderón-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 geometrical optics solutions which reduce the Calderón-type problem to a tomography problem for 2-tensors. The arguments in this paper allow us to establish partial data results for elliptic systems that generalize the scalar results due to Kenig, Sjöstrand and Uhlmann.
PublisherMathematical Sciences Publishers
Publication in research information system
MetadataShow full item record
Showing items with similar title or keywords.
Covi, Giovanni; Rüland, Angkana (Elsevier, 2021)In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal ...
Chung, Francis J.; Ola, Petri; Salo, Mikko; Tzou, Leo (Elsevier, 2018)In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary ...
Ghosh, Tuhin; Salo, Mikko; Uhlmann, Gunther (Mathematical Sciences Publishers, 2020)We show global uniqueness in an inverse problem for the fractional Schrödinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness ...
Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications 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 ...
Guillarmou, Colin; Salo, Mikko; Tzou, Leo (Springer, 2019)In this note we show that on any compact subdomain of a K¨ahler manifold that admits sufficiently many global holomorphic functions, the products of harmonic functions form a complete set. This gives a positive answer to ...