Geodesic
Nonunique continuation for the Maxwell system
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 41, Tome 393 (2011), pp. 80-100 Cet article a éte moissonné depuis la source Math-Net.Ru

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We give an example of the stationary Maxwell system, which has nontrivial smooth solution with compact support; the coefficients $\varepsilon,\mu$ belong to $C^\alpha$ for all $\alpha<1$. Our example shows that the stationary Maxwell system does not possess the unique continuation property in case of nonsmooth coefficients. 
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     author = {M. N. Demchenko},
     title = {Nonunique continuation for the {Maxwell} system},
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}
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M. N. Demchenko. Nonunique continuation for the Maxwell system. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 41, Tome 393 (2011), pp. 80-100. http://geodesic.mathdoc.fr/item/ZNSL_2011_393_a5/

[1] M. Eller, M. Yamamoto, “A Carleman inequality for the stationary anisotropic Maxwell system”, J. Math. Pures Appl., 86 (2006), 449–462 | DOI | MR | Zbl

[2] T. Suslina, “Absolyutnaya nepreryvnost spektra periodicheskogo operatora Maksvella v sloe”, Zap. nauchn. semin. POMI, 288, 2002, 232–255 | MR | Zbl

[3] N. Filonov, “Ellipticheskoe uravnenie vtorogo poryadka v divergentnoi forme, imeyuschee reshenie s kompaktnym nositelem”, Problemy mat. analiza, 22, 2001, 246–257 | Zbl

[4] K. Miller, “Nonunique continuation for uniformly parabolic and elliptic equations in self-adjoint divergence form with Hölder continuous coefficients”, Arch. Rat. Mech Anal., 54:2 (1974), 105–117 | DOI | MR | Zbl

[5] A. Pliŝ, “On non-uniqueness in Cauchy problem for an elliptic second order equation”, Bull. de l'Acad. Polon. Sc., Série Sc., Math., Astr., Phys., 11:3 (1963), 95–100 | MR | Zbl