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On the non-vanishing property for real analytic solutions of the $ p$-Laplace equation


Author: Vladimir G. Tkachev
Journal: Proc. Amer. Math. Soc. 144 (2016), 2375-2382
MSC (2010): Primary 17A30, 35J92; Secondary 17C27
DOI: https://doi.org/10.1090/proc/12912
Published electronically: October 21, 2015
MathSciNet review: 3477054
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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} \vert Du\vert^{p-2}Du(x)=0 $ in $ \mathbb{R}^{n}$ for any $ n\ge 2$ and $ p\not \in \{1,2\}$.


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Additional Information

Vladimir G. Tkachev
Affiliation: Department of Mathematics, Linköping University, Sweden
Email: vladimir.tkatjev@liu.se

DOI: https://doi.org/10.1090/proc/12912
Keywords: $p$-Laplace equation, non-associative algebras, idempotents, Peirce decompositions, $p$-harmonic functions
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
Article copyright: © Copyright 2015 American Mathematical Society