Removable sets for continuous solutions of quasilinear elliptic equations
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- by Tero Kilpeläinen and Xiao Zhong PDF
- Proc. Amer. Math. Soc. 130 (2002), 1681-1688 Request permission
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.References
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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
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1681-1688
- MSC (2000): Primary 35J60, 35J70, 30C65
- DOI: https://doi.org/10.1090/S0002-9939-01-06237-2
- MathSciNet review: 1887015