Geodesic
Double-sided estimates for eigenfrequencies in the John problem for freely floating body
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 42, Tome 397 (2011), pp. 89-114

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The two-dimensional problem on oblique incident waves and a freely floating cylinder is reduced to the study of the spectrum of a suitable self-adjoint operator in Hilbert space. Using tools from spectral measure theory we estimate the difference between eigenfrequencies of the original problem and a problem on an inert body, which does not react to the buoyancy forces. We give the localization of eigenfrequencies of the freely floating body, and in addition derive a sufficient condition for the existence of the point spectrum in the corresponding boundary value problem. 
@article{ZNSL_2011_397_a4,
     author = {S. A. Nazarov and J. Taskinen},
     title = {Double-sided estimates for eigenfrequencies in the {John} problem for freely floating body},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {89--114},
     publisher = {mathdoc},
     volume = {397},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_397_a4/}
}
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S. A. Nazarov; J. Taskinen. Double-sided estimates for eigenfrequencies in the John problem for freely floating body. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 42, Tome 397 (2011), pp. 89-114. http://geodesic.mathdoc.fr/item/ZNSL_2011_397_a4/