Harmonic homeomorphisms of the closed disc to itself need be in $W^\{1,p\}$, $p<2$, but not $W^\{1,2\}$
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Abstract:
Harmonic maps $u$ from the closed disc onto bounded convex sets of the plane obey $u\in W^{1,p}, p<2$.References
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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
- 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
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 891-894
- MSC (2000): Primary 58E20, 46E35
- DOI: https://doi.org/10.1090/S0002-9939-06-08506-6
- MathSciNet review: 2262887