6533b7d6fe1ef96bd1265cdf
RESEARCH PRODUCT
The Poisson embedding approach to the Calderón problem
Mikko SaloTony LiimatainenMatti Lassassubject
Pure mathematicsRIEMANNIAN-MANIFOLDSDEVICESGeneral MathematicsBoundary (topology)INVISIBILITYPoisson distribution01 natural sciencesinversio-ongelmatsymbols.namesakeMathematics - Analysis of PDEs0103 physical sciences111 MathematicsREGULARITYUniqueness0101 mathematicsEQUATIONSMathematicsosittaisdifferentiaaliyhtälötCalderón problemCLOAKING010102 general mathematicsRiemannian manifoldInverse problemFULLManifoldPoisson embeddingHarmonic functionsymbolsEmbedding010307 mathematical physics35R30 (Primary) 35J25 53C21(Secondary)INVERSE PROBLEMSdescription
We introduce a new approach to the anisotropic Calder\'on problem, based on a map called Poisson embedding that identifies the points of a Riemannian manifold with distributions on its boundary. We give a new uniqueness result for a large class of Calder\'on type inverse problems for quasilinear equations in the real analytic case. The approach also leads to a new proof of the result by Lassas and Uhlmann (2001) solving the Calder\'on problem on real analytic Riemannian manifolds. The proof uses the Poisson embedding to determine the harmonic functions in the manifold up to a harmonic morphism. The method also involves various Runge approximation results for linear elliptic equations.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-01-01 | Mathematische Annalen |