Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An elliptic regularity coefficient estimate for a problem arising from a frequency domain treatment of waves
HTML articles powered by AMS MathViewer

by Xiaobing Feng and Dongwoo Sheen PDF
Trans. Amer. Math. Soc. 346 (1994), 475-487 Request permission

Abstract:

We consider a sequence of noncoercive elliptic problems, which are the wave equation in the frequency domain, in a rectangular or cubic domain with an absorbing boundary condition. The elliptic regularity coefficient depends on the frequency, and it has a singularity for both zero and infinite frequency. In this paper we derive an elliptic regularity estimate as the frequency tends to zero and infinity.
References
  • Robert A. Adams, Sobolev spaces, Pure and Applied Mathematics, Vol. 65, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0450957
  • A.-P. Calderón, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), no. 4, 1324–1327. MR 466568, DOI 10.1073/pnas.74.4.1324
  • R. R. Coifman, A. McIntosh, and Y. Meyer, L’intégrale de Cauchy définit un opérateur borné sur $L^{2}$ pour les courbes lipschitziennes, Ann. of Math. (2) 116 (1982), no. 2, 361–387 (French). MR 672839, DOI 10.2307/2007065
  • Jim Douglas Jr., Dongwoo Sheen, and Juan E. Santos, Approximation of scalar waves in the space-frequency domain, Math. Models Methods Appl. Sci. 4 (1994), no. 4, 509–531. MR 1291136, DOI 10.1142/S0218202594000297
  • Jim Douglas Jr., Juan E. Santos, Dongwoo Sheen, and Lynn Schreyer Bennethum, Frequency domain treatment of one-dimensional scalar waves, Math. Models Methods Appl. Sci. 3 (1993), no. 2, 171–194. MR 1212938, DOI 10.1142/S0218202593000102
    • X. Feng, An elliptic regularity coefficient estimate for the equations of the motion for nearly elastic solids in the frequency domain, Comp. Appl. Math. (accepted).
  • P. Grisvard, Singularities in boundary value problems, Recherches en Mathématiques Appliquées [Research in Applied Mathematics], vol. 22, Masson, Paris; Springer-Verlag, Berlin, 1992. MR 1173209
    • C. L. Ravazzoli, J. Douglas, Jr., J. E. Santos, and D. Sheen, On the solution of the equations of motion for nearly elastic solids in the frequency domain, preprint. C. J. Tarnter, Bessel functions with some applications, Hart, New York, 1969.
  • Gregory Verchota, Layer potentials and regularity for the Dirichlet problem for Laplace’s equation in Lipschitz domains, J. Funct. Anal. 59 (1984), no. 3, 572–611. MR 769382, DOI 10.1016/0022-1236(84)90066-1
  • G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 35L05, 35B40, 35J99
  • Retrieve articles in all journals with MSC: 35L05, 35B40, 35J99
Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 346 (1994), 475-487
  • MSC: Primary 35L05; Secondary 35B40, 35J99
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1282886-6
  • MathSciNet review: 1282886