Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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.


Diffusion d’une onde par un coin
HTML articles powered by AMS MathViewer

by Patrick Gérard and Gilles Lebeau
J. Amer. Math. Soc. 6 (1993), 341-424


We study the Dirichlet problem for a wave outside a corner with general analytic boundary. In particular, we give the asymptotic expansion of the singularity on the diffracted cone.
  • M. S. Baouendi and C. Goulaouic, Remarks on the abstract form of nonlinear Cauchy-Kovalevsky theorems, Comm. Partial Differential Equations 2 (1977), no. 11, 1151–1162. MR 481322, DOI 10.1080/03605307708820057
  • J. Cheeger and M. Taylor, Diffraction by conical singularities. I, Comm. Pure Appl. Math. 35 (1982), 275-331; II, Comm. Pure Appl. Math. 35 (1982), 487-529.
  • H. G. Garnir, Fonctions de Green de l’opérateur métaharmonique pour les problèmes de Dirichlet et de Neumann posés dans un angle ou un dièdre, Bull. Soc. Roy. Sci. Liège 21 (1952), 119–140, 207–231 (French). MR 56811
  • P. Grisvard, Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics, vol. 24, Pitman (Advanced Publishing Program), Boston, MA, 1985. MR 775683
  • L. Hörmander, The analysis of linear partial differential operators, Vol. 3, Springer, Berlin and New York, 1985.
  • Masaki Kashiwara and Takahiro Kawai, Micro-hyperbolic pseudo-differential operators. I, J. Math. Soc. Japan 27 (1975), no. 3, 359–404. MR 377998, DOI 10.2969/jmsj/02730359
  • Joseph B. Keller, Geometrical theory of diffraction, J. Opt. Soc. Amer. 52 (1962), 116–130. MR 135064, DOI 10.1364/JOSA.52.000116
  • G. Lebeau, Deuxième microlocalisation à croissance, Goulaouic-Meyer-Schwartz Seminar, 1982/1983, École Polytech., Palaiseau, 1983, pp. Exp. No. 15, 10 (French). MR 716903
  • Gilles Lebeau, Deuxième microlocalisation sur les sous-variétés isotropes, Ann. Inst. Fourier (Grenoble) 35 (1985), no. 2, 145–216 (French, with English summary). MR 786539, DOI 10.5802/aif.1014
  • H. M. Macdonald, Electric waves, Cambridge University Press, London and New York, 1902, pp. 186-198. F. Molinet, Geometrical theory of diffraction. I, IEEE Antennas and Propagation Society Newsletter, August 1987, pp. 6-17; II, IEEE Antennas and Propagation Society Newsletter, October 1987, pp. 5-16.
  • L. Nirenberg, An abstract form of the nonlinear Cauchy-Kowalewski theorem, J. Differential Geometry 6 (1972), 561–576. MR 322321, DOI 10.4310/jdg/1214430643
  • L. V. Ovsjannikov, A nonlinear Cauchy problem in a scale of Banach spaces, Dokl. Akad. Nauk SSSR 200 (1971), 789–792 (Russian). MR 0285941
  • Michel Rouleux, Diffraction analytique sur une variété à singularité conique, Comm. Partial Differential Equations 11 (1986), no. 9, 947–988 (French). MR 844171, DOI 10.1080/03605308608820452
  • Pierre Schapira, Propagation at the boundary and reflection of analytic singularities of solutions of linear partial differential equations. I, Proceedings of the Oji Seminar on Algebraic Analysis and the RIMS Symposium on Algebraic Analysis (Kyoto Univ., Kyoto, 1976), 1976/77, pp. 441–453. MR 0494317, DOI 10.2977/prims/1195196619
  • Johannes Sjöstrand, Propagation of analytic singularities for second order Dirichlet problems, Comm. Partial Differential Equations 5 (1980), no. 1, 41–93. MR 556454, DOI 10.1080/03605308008820133
  • Johannes Sjöstrand, Singularités analytiques microlocales, Astérisque, 95, Astérisque, vol. 95, Soc. Math. France, Paris, 1982, pp. 1–166 (French). MR 699623
  • Johannes Sjöstrand, Analytic singularities and microhyperbolic boundary value problems, Math. Ann. 254 (1980), no. 3, 211–256. MR 597081, DOI 10.1007/BF01457998
  • Motoo Uchida, Microlocal analysis of diffraction by a corner, Ann. Sci. École Norm. Sup. (4) 25 (1992), no. 1, 47–75. MR 1152613, DOI 10.24033/asens.1643
  • Jean-Pierre Varenne, Diffraction par un angle ou un dièdre, C. R. Acad. Sci. Paris Sér. A-B 290 (1980), no. 4, A175–A178 (French, with English summary). MR 564154, DOI 10.1002/cpa.3160350302
Similar Articles
Bibliographic Information
  • © Copyright 1993 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 6 (1993), 341-424
  • MSC: Primary 35L05; Secondary 35A27, 35B40, 35S15, 58G07
  • DOI:
  • MathSciNet review: 1157289