Three-spheres theorems for subelliptic quasilinear equations in Carnot groups of Heisenberg-type
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Abstract:
We study the arithmetic three-spheres theorems for subsolutions of subelliptic PDEs of $p$-harmonic type in Carnot groups of Heisenberg type for $1<p<\infty$. In the presentation we exhibit the special cases of sub-Laplace equations ($p=2$) and the case $p$ is equal to the homogeneous dimension of a Carnot group. Corollaries include asymptotic behavior of subsolutions for small and large radii and the Liouville-type theorems.References
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Additional Information
- Tomasz Adamowicz
- Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warsaw, Poland
- MR Author ID: 815631
- Email: T.Adamowicz@impan.pl
- Ben Warhurst
- Affiliation: Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland
- MR Author ID: 724691
- Email: B.Warhurst@mimuw.edu.pl
- Received by editor(s): August 4, 2015
- Received by editor(s) in revised form: November 27, 2015
- Published electronically: March 25, 2016
- Communicated by: Jeremy T. Tyson
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4291-4302
- MSC (2010): Primary 35H20; Secondary 31C15, 53C17
- DOI: https://doi.org/10.1090/proc/13050
- MathSciNet review: 3531180