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- W4387162063 abstract "We are concerned with the unique continuation property (UCP) of the time-harmonic Maxwell system $$displaystyle nabla wedge mathbf {E}-mathrm {i} kmathbf {H}={mathbf 0},, quad nabla wedge mathbf {H}+mathrm {i} kmathbf {E}={mathbf 0} quad mbox{in} ~~varOmega , $$ where $$mathrm {i}:=sqrt {-1}$$ and $$kin mathbb {R}_+$$ , in a particular scenario that is strongly motivated by our study of the inverse electromagnetic scattering problem. In this chapter, we follow the treatment in Diao et al. (Inverse Probl 37:035004, 2021). Further discussion on the inverse electromagnetic scattering problems can be found in Sect. 4.1.2 . We start with the necessary mathematical setup. We consider the domain Ω to be an open set in $$mathbb {R}^3$$ , bounded or unbounded, and the solution (E, H) to the system (3.1.1) in the space Hloc(curl, Ω) defined by $$displaystyle begin {array}{rl} H_{loc}(mathrm {curl}, varOmega )=& big {U|{ }_{B}in H(mathrm {curl}, B); B mbox{is any bounded subdomain of} varOmega big }, H(mathrm {curl}, B)=& big {Uin L^2(B)^3; nabla wedge Uin L^2(B)^3big }. end {array} $$" @default.
- W4387162063 created "2023-09-30" @default.
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- W4387162063 date "2023-01-01" @default.
- W4387162063 modified "2023-09-30" @default.
- W4387162063 title "Geometric Structures of Maxwellian Eigenfunctions" @default.
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- W4387162063 doi "https://doi.org/10.1007/978-3-031-34615-6_3" @default.
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