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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.

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On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles
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by Kunio Hidano, Jason Metcalfe, Hart F. Smith, Christopher D. Sogge and Yi Zhou PDF
Trans. Amer. Math. Soc. 362 (2010), 2789-2809 Request permission


We establish the Strauss conjecture concerning small-data global existence for nonlinear wave equations, in the setting of exterior domains to compact obstacles, for space dimensions $n=3$ and $4$. The obstacle is assumed to be nontrapping, and the solution is assumed to satisfy either Dirichlet or Neumann conditions along the boundary of the obstacle. The key step in the proof is establishing certain “abstract Strichartz estimates” for the linear wave equation on exterior domains.
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Additional Information
  • Kunio Hidano
  • Affiliation: Department of Mathematics, Mie University, Mie Prefecture, Japan
  • Jason Metcalfe
  • Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3260
  • MR Author ID: 733199
  • Hart F. Smith
  • Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-4350
  • Christopher D. Sogge
  • Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21244
  • MR Author ID: 164510
  • Yi Zhou
  • Affiliation: School of Mathematical Science, Fudan University, Shanghai, People’s Republic of China
  • Received by editor(s): February 13, 2009
  • Published electronically: December 8, 2009
  • Additional Notes: The first author was supported in part by the Grant-in-Aid for Young Scientists (B) (No. 18740069), The Ministry of Education, Culture, Sports, Science and Technology, Japan, and he would like to thank the Department of Mathematics at the Johns Hopkins University for the hospitality and financial support during his visit where part of this research was carried out
    The second, third and fourth authors were supported by the National Science Foundation
    The fifth author was supported by project 10728101 of NSFC and the “111” project and Doctoral Programme Foundation of the Ministry of Education of China.
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 362 (2010), 2789-2809
  • MSC (2000): Primary 35L05, 35L20, 35L71
  • DOI:
  • MathSciNet review: 2584618