6533b7d1fe1ef96bd125cca6

RESEARCH PRODUCT

Partial data inverse problems for Maxwell equations via Carleman estimates

Petri OlaLeo TzouMikko SaloFrancis J. Chung

subject

Inverse problemsELECTRODYNAMICSINFORMATIONadmissible manifoldsWEIGHTSMathematics::Analysis of PDEsBoundary (topology)InverseBOUNDARY-VALUE PROBLEMCALDERON PROBLEMpartial data01 natural sciencesMATERIAL PARAMETERSinversio-ongelmatsymbols.namesakeMathematics - Analysis of PDEsFOS: Mathematics35R30 35Q61111 MathematicsMaxwellin yhtälötBoundary value problemUniqueness0101 mathematicsPartial dataMathematical PhysicsMathematicsAdmissible manifoldsApplied Mathematicsta111010102 general mathematicsMathematical analysisScalar (physics)Inverse problemCarleman estimatesSmall set010101 applied mathematicsUNIQUENESSMaxwell's equationsMaxwell equationsLOCAL DATAsymbolsAnalysisAnalysis of PDEs (math.AP)

description

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 data is measured on a possibly very small set. This is an extension of earlier scalar results of Bukhgeim-Uhlmann and Kenig-Sj\"ostrand-Uhlmann to the Maxwell system. The main contribution is to show that the Carleman estimate approach to scalar partial data inverse problems introduced in those works can be carried over to the Maxwell system.

yearjournalcountryeditionlanguage
2015-02-05
10.1016/j.anihpc.2017.06.005http://hdl.handle.net/10138/313514