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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Harmonic homeomorphisms of the closed disc to itself need be in $ W^{1,p}$, $ p<2$, but not $ W^{1,2}$


Author: Gregory C. Verchota
Journal: Proc. Amer. Math. Soc. 135 (2007), 891-894
MSC (2000): Primary 58E20, 46E35
Published electronically: August 28, 2006
MathSciNet review: 2262887
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Abstract: Harmonic maps $ u$ from the closed disc onto bounded convex sets of the plane obey $ u\in W^{1,p}, p<2$.


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Additional Information

Gregory C. Verchota
Affiliation: Department of Mathematics, 215 Carnegie, Syracuse University, Syracuse, New York 13244
Email: gverchot@syr.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08506-6
PII: S 0002-9939(06)08506-6
Received by editor(s): June 6, 2005
Received by editor(s) in revised form: September 26, 2005
Published electronically: August 28, 2006
Additional Notes: The author thanks Tadeusz Iwaniec for this question.
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2006 American Mathematical Society