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Proceedings of the American Mathematical Society

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Maximal smoothness for solutions to equilibrium equations in 2D nonlinear elasticity


Author: Xiaodong Yan
Journal: Proc. Amer. Math. Soc. 135 (2007), 1717-1724
MSC (2000): Primary 35B65
DOI: https://doi.org/10.1090/S0002-9939-06-08645-X
Published electronically: November 15, 2006
MathSciNet review: 2286081
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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

DOI: https://doi.org/10.1090/S0002-9939-06-08645-X
Keywords: Equilibrium equations, weak solution, maximal smoothness
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
Article copyright: © Copyright 2006 American Mathematical Society