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

Author(s): Xiaodong Yan
Journal: Proc. Amer. Math. Soc. 135 (2007), 1717-1724.
MSC (2000): Primary 35B65
Posted: November 15, 2006
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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: 10.1090/S0002-9939-06-08645-X
PII: S 0002-9939(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
Posted: 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 of article: Copyright 2006, American Mathematical Society

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