Free Access
Volume 45, Number 5, September-October 2011
Page(s) 947 - 979
Published online 27 May 2011
  1. F.L. Bakharev and S.A. Nazarov, On the structure of the spectrum of the elasticity problem for a body with a super-sharp spike. Sibirsk. Mat. Zh. 50 (2009) 746–756. (English transl. Siberian Math. J. 50 (2009).) [Google Scholar]
  2. M.S. Birman and M.Z. Solomyak, Spectral theory of self–adjoint operators in Hilber space. Reidel Publ. Company, Dordrecht (1986). [Google Scholar]
  3. A.-S. Bonnet-Ben Dhia, P. Joly, Mathematical analysis of guided water waves. SIAM J. Appl. Math. 53 (1993). [Google Scholar]
  4. G. Cardone, S.A. Nazarov and J. Sokolowski, Asymptotics of solutions of the Neumann problem in a domain with closely posed components of the boundary. Asymptotic Analysis 62 (2009) 41–88. [MathSciNet] [Google Scholar]
  5. G. Cardone, S.A. Nazarov and J. Taskinen, The “absorption" effect caused by beak-shaped boundary irregularity for elastic waves. Dokl. Ross. Akad. Nauk. 425 (2009) 182–186. (English transl. Doklady Physics 54 (2009) 146–150.) [Google Scholar]
  6. G. Cardone, S.A. Nazarov and J. Taskinen, Criteria for the existence of the essential spectrum for beak–shaped elastic bodies. J. Math. Pures Appl. (to appear) [Google Scholar]
  7. D. Daners, Robin boundary value problems on arbitrary domains. Trans. Amer. Math. Soc. 352 (2000) 4207–4236. [Google Scholar]
  8. D. Daners, A Faber-Krahn inequality for Robin problems in any space dimension. Math. Annal. 335 (2006) 767–785. [Google Scholar]
  9. D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order. Die Grundlehren der mathematischen Wissenschaften 224. Springer, Berlin (1977). [Google Scholar]
  10. D.S. Jones, The eigenvalues of Formula when the boundary conditions are given on semi-infinite domains. Proc. Camb. Phil. Soc. 49 (1953) 668–684. [Google Scholar]
  11. V.A. Kondratiev, Boundary value problems for elliptic problems in domains with conical or corner points. Trudy Moskov. Mat. Obshch. 16 (1967) 209–292. (English transl. Trans. Moscow Mat. Soc. 16 (1967) 227–313.) [Google Scholar]
  12. V.A. Kozlov, V.G. Maz'ya and J. Rossmann, Elliptic boundary value problems in domains with point singularities. Mathematical Surveys and Monographs 52. American Mathematical Society, Providence, RI (1997). [Google Scholar]
  13. V.A. Kozlov, V.G. Maz'ya and J. Rossmann, Spectral problems associated with corner singularities of solutions to elliptic equations. Mathematical Surveys and Monographs 85. American Mathematical Society, Providence, RI (2001). [Google Scholar]
  14. V.V. Krylov, New type of vibration dampers utilising the effect of acoustic “black holes". Acta Acustica united with Acustica 90 (2004) 830–837. [Google Scholar]
  15. N. Kuznetsov, V. Maz'ya and B. Vainberg, Linear Water Waves. Cambridge University Press, Cambridge (2002). [Google Scholar]
  16. O.A. Ladyzhenskaya, Boundary value problems of mathematical physics. Springer Verlag, New York (1985). [Google Scholar]
  17. J.L. Lions and E. Magenes, Non-homogeneus boundary value problems and applications (French). Dunod, Paris (1968). (English transl. Springer-Verlag, Berlin-Heidelberg-New York (1972).) [Google Scholar]
  18. V. Mazya, Sobolev spaces, translated from the Russian by T.O. Shaposhnikova. Springer Series in Soviet Mathematics. Springer-Verlag, Berlin (1985). [Google Scholar]
  19. V.G. Maz'ya and B.A. Plamenevskii, The asymptotic behavior of solutions of differential equations in Hilbert space. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972) 1080–1133; erratum, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 709–710. [Google Scholar]
  20. V.G, Mazja and B.A. Plamenevskii, On coefficients in asymptotics of solutions of elliptic boundary value problems in a domain with conical points. Math. Nachr. 76 (1977) 29–60. (Engl. transl. Amer. Math. Soc. Transl. 123 (1984) 57–89.) [CrossRef] [MathSciNet] [Google Scholar]
  21. V.G. Mazja and B.A. Plamenevskii, Estimates in Lp and Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary. Math. Nachr. 81 (1978) 25–82. (Engl. transl. Amer. Math. Soc. Transl. (Ser. 2) 123 (1984) 1–56 .) [CrossRef] [MathSciNet] [Google Scholar]
  22. V.G. Mazya and S.V. Poborchi, Imbedding and Extension Theorems for Functions on Non-Lipschitz Domains. SPbGU publishing (2006). [Google Scholar]
  23. M.A. Mironov, Propagation of a flexural wave in a plate whose thickness decreases smoothly to zero in a finite interval. Soviet Physics-Acoustics 34 (1988) 318–319. [Google Scholar]
  24. S.A. Nazarov Asymptotics of the solution of the Neumann problem at a point of tangency of smooth components of the boundary of the domain. Izv. Ross. Akad. Nauk. Ser. Mat. 58 (1994) 92–120. (English transl. Math. Izvestiya 44 (1995) 91–118.) [Google Scholar]
  25. S.A. Nazarov, On the flow of water under a still stone. Mat. Sbornik 186 (1995) 75–110. (English transl. Math. Sbornik 186 (1995) 1621–1658.) [Google Scholar]
  26. S.A. Nazarov, A general scheme for averaging self-adjoint elliptic systems in multidimensional domains, including thin domains. Algebra Analiz. 7 (1995) 1–92. (English transl. St. Petersburg Math. J. 7 (1996) 681–748.) [MathSciNet] [Google Scholar]
  27. S.A. Nazarov, The polynomial property of self-adjoint elliptic boundary-value problems and the algebraic description of their attributes. Uspehi Mat. Nauk. 54 (1999) 77–142. (English transl. Russ. Math. Surveys. 54 (1999) 947–1014.) [Google Scholar]
  28. S.A. Nazarov, Weighted spaces with detached asymptotics in application to the Navier-Stokes equations. in: Advances in Mathematical Fluid Mechanics. Paseky, Czech. Republic (1999) 159–191. Springer-Verlag, Berlin (2000). [Google Scholar]
  29. S.A. Nazarov, The Navier-Stokes problem in a two-dimensional domain with angular outlets to infinity. Zap. Nauchn. Sem. St.-Petersburg Otdel. Mat. Inst. Steklov 257 (1999) 207–227. (English transl. J. Math. Sci. 108 (2002) 790–805.) [Google Scholar]
  30. S.A. Nazarov, The spectrum of the elasticity problem for a spiked body. Sibirsk. Mat. Zh. 49 (2008) 1105–1127. (English transl. Siberian Math. J. 49 (2008) 874–893.) [Google Scholar]
  31. S.A. Nazarov, On the spectrum of the Steklov problem in peak-shaped domains. Trudy St.-Petersburg Mat. Obshch. 14 (2008) 103–168. (English transl. Am. Math. Soc. Transl Ser. 2.) [Google Scholar]
  32. S.A. Nazarov. On the essential spectrum of boundary value problems for systems of differential equations in a bounded peak-shaped domain. Funkt. Anal. i Prilozhen. 43 (2009) 55–67. (English transl. Funct. Anal. Appl. 43 (2009).) [Google Scholar]
  33. S.A. Nazarov and K. Pileckas, On steady Stokes and Navier-Stokes problems with zero velocity at infinity in a three-dimensional exterior domain. Journal of Mathematics of Kyoto University 40 (2000) 475–49. [MathSciNet] [Google Scholar]
  34. S.A. Nazarov and B.A. Plamenevskii, Radiation principles for self-adjoint elliptic problems. Probl. Mat. Fiz. 13. 192–244. Leningrad: Leningrad Univ. 1991 (Russian). [Google Scholar]
  35. S.A. Nazarov and B.A. Plamenevskii, Elliptic problems in domains with piecewise smooth boundaries. Walter be Gruyter, Berlin, New York (1994). [Google Scholar]
  36. S.A. Nazarov and O.R. Polyakova, Asymptotic behavior of the stress-strain state near a spatial singularity of the boundary of the beak tip type. Prikl. Mat. Mekh. 57 (1993) 130–149. (English transl. J. Appl. Math. Mech. 57 (1993) 887–902.) [Google Scholar]
  37. S.A. Nazarov and S.A. Taskinen, On the spectrum of the Steklov problem in a domain with a peak. Vestnik St. Petersburg Univ. Math. 41 (2008) 45–52. [CrossRef] [MathSciNet] [Google Scholar]
  38. S.A. Nazarov and J. Taskinen, On essential and continuous spectra of the linearized water-wave problem in a finite pond. Math. Scand. 106 (2009) 1–20. [Google Scholar]
  39. J. Peetre, Another approach to elliptic boundary problems. Comm. Pure. Appl. Math. 14 (1961) 711–731. [Google Scholar]
  40. B.A. Plamenevskii, The asymptotic behavior of the solutions of quasielliptic differential equations with operator coefficients. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 1332–1375. [Google Scholar]
  41. J.J. Stoker, Water waves. The Mathematical Theory with Applications. Reprint of the 1957 original. John Wiley, New York (1992). [Google Scholar]
  42. F. Ursell, Trapping modes in the theory of surface waves. Proc. Camb. Phil. Soc. 47 (1951) 347–358. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you