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Rosetta
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Shape Identification in Inverse Medium Scattering Problems
Consider time-harmonic acoustic scattering from a bounded penetrable obstacle D C RN embedded in a homogeneous background medium. The index of refraction characterizing the material inside D is supposed to be Hölder continuous near the corners. If D C R2 is a convex polygon, we prove that its shape and location can be uniquely determined by the far-field pattern incited by a single incident wave at a fixed frequency. In dimensions N ≥ 3, the uniqueness applies to penetrable scatterers of rectangular type with additional assumptions on the smoothness of the contrast. Our arguments are motivated by recent studies on the absence of non-scattering wavenumbers in domains with corners. As a byproduct, we show that the smoothness conditions in previous corner scattering results are only required near the corners.
Medium Companies of Europe 1992/93
Volumes 1 & 2 Guide to the MEDIUM COMPANIES OF EUROPE 1992/93, Volume 1, arrangement of the book contains useful information on nearly 4500 of the most important medium-sized companies in the European This book has been arranged in order to allow the reader to Community, excluding the UK, over 1500 companies of which find any entry rapidly and accurately. are covered in Volume 2. Volume 3 covers nearly 2000 of the medium-sized companies within Western Europe but outside Company entries are listed alphabetically within each country the European Community. Altogether the three volumes of section; in addition three indexes are provided in Volumes 1 MEDIUM COMPANIES OF EUROPE now provide in and ...
Quantitative Flatness Results and BV -estimates for Stable Nonlocal Minimal Surfaces
We establish quantitative properties of minimizers and stable sets for nonlocal interaction functionals, including the s-fractional perimeter as a particular case. On the one hand, we establish universal BV -estimates in every dimension n> 2 for stable sets. Namely, we prove that any stable set in B1 has finite classical perimeter in B1/2, with a universal bound. This nonlocal result is new even in the case of s-perimeters and its local counterpart (for classical stable minimal surfaces) was known only for simply connected two-dimensional surfaces immersed in R3. On the other hand, we prove quantitative flatness estimates for minimizers and stable sets in low dimensions n = 2, 3. More precisely, we show that a stable set in BR, with R large, is very close in measure to being a half space in B1 -with a quantitative estimate on the measure of the symmetric difference. As a byproduct, we obtain new classification results for stable sets in the whole plane.
ESA Achievements
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Suomen kemistilehti
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