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

 

Removable sets for continuous solutions of quasilinear elliptic equations


Authors: Tero Kilpeläinen and Xiao Zhong
Journal: Proc. Amer. Math. Soc. 130 (2002), 1681-1688
MSC (2000): Primary 35J60, 35J70, 30C65
Published electronically: October 24, 2001
MathSciNet review: 1887015
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Abstract: We show that sets of $n-p+\alpha (p-1)$ Hausdorff measure zero are removable for $\alpha $-Hölder continuous solutions to quasilinear elliptic equations similar to the $p$-Laplacian. The result is optimal. We also treat larger sets in terms of a growth condition. In particular, our results apply to quasiregular mappings.


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Additional Information

Tero Kilpeläinen
Affiliation: Department of Mathematics, University of Jyväskylä, P.O. Box 35, 40351 Jyväskylä, Finland
Email: terok@math.jyu.fi

Xiao Zhong
Affiliation: Department of Mathematics, University of Jyväskylä, P.O. Box 35, 40351 Jyväskylä, Finland
Email: zhong@math.jyu.fi

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06237-2
PII: S 0002-9939(01)06237-2
Keywords: $p$-Laplacian, equations involving measures, removable sets, quasiregular mappings
Received by editor(s): September 13, 2000
Received by editor(s) in revised form: December 1, 2000
Published electronically: October 24, 2001
Additional Notes: This research was supported by the Academy of Finland (Project #41964).
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2001 American Mathematical Society