ISSN:
1432-0673
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract Suppose the 3-dimensional space is filled with three materials having dielectric constants ɛ 1 above S 1={x 2=f 1(x 1), x 3 arbitrary}, ɛ 2 below S 2 = {x 2 =f 2(x 1), x 3 arbitrary} and ɛ o in {f 2(x 1) 〈x 2 〈f1(x 1), x 3 arbitrary} where f 1 f 2 are periodic functions. Suppose for a plane wave incident on S 1 from above we can measure the reflected and transmitted waves of the corresponding time-harmonic solution of the Maxwell equations, say at x 2=±b,b large. To what extent can we infer from these measurements the location of the pair (S 1, S 2 ? In this paper, we establish a local stability: If ( $$\tilde S_1 ,\tilde S_2$$ ) is another pair of periodic curves “close” to (S 1, S2), then, for any δ〉0, if the measurements for the two pairs are δ-close, then $$\tilde S_1$$ and $$\tilde S_2$$ are 0(δ)-close to S 1 and S 2, respectively.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00390349
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