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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Maximal smoothness for solutions to equilibrium equations in 2D nonlinear elasticity
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by Xiaodong Yan PDF
Proc. Amer. Math. Soc. 135 (2007), 1717-1724 Request permission

Abstract:

For a class of variational integrals from 2D nonlinear elasticity, we prove that any $W^{2,2}\cap C^{1}$weak solution for the equilibrium equations is smooth. Moreover, we present an example showing that the assumption $u\in$ $W^{2,2}$ is optimal.
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Additional Information
  • Xiaodong Yan
  • Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
  • Email: xiayan@math.msu.edu
  • Received by editor(s): August 10, 2005
  • Received by editor(s) in revised form: December 22, 2005
  • Published electronically: November 15, 2006
  • Additional Notes: This research was partially supported by NSF grant DMS-0431710 and IRGP grant from Michigan State University.
  • Communicated by: David S. Tartakoff
  • © Copyright 2006 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 1717-1724
  • MSC (2000): Primary 35B65
  • DOI: https://doi.org/10.1090/S0002-9939-06-08645-X
  • MathSciNet review: 2286081