On the non-vanishing property for real analytic solutions of the $p$-Laplace equation
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- by Vladimir G. Tkachev
- Proc. Amer. Math. Soc. 144 (2016), 2375-2382
- DOI: https://doi.org/10.1090/proc/12912
- Published electronically: October 21, 2015
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Abstract:
By using a non-associative algebra argument, we prove that $u\equiv 0$ is the only cubic homogeneous polynomial solution to the $p$-Laplace equation $\mathrm {div} |Du|^{p-2}Du(x)=0$ in $\mathbb {R}^{n}$ for any $n\ge 2$ and $p\not \in \{1,2\}$.References
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Bibliographic Information
- Vladimir G. Tkachev
- Affiliation: Department of Mathematics, Linköping University, Sweden
- MR Author ID: 246080
- Email: vladimir.tkatjev@liu.se
- Received by editor(s): March 11, 2015
- Received by editor(s) in revised form: July 23, 2015
- Published electronically: October 21, 2015
- Communicated by: Joachim Krieger
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2375-2382
- MSC (2010): Primary 17A30, 35J92; Secondary 17C27
- DOI: https://doi.org/10.1090/proc/12912
- MathSciNet review: 3477054