Three-spheres theorems for subelliptic quasilinear equations in Carnot groups of Heisenberg-type

Adamowicz, Tomasz; Warhurst, Ben

doi:10.1090/proc/13050

Three-spheres theorems for subelliptic quasilinear equations in Carnot groups of Heisenberg-type
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by Tomasz Adamowicz and Ben Warhurst PDF

Proc. Amer. Math. Soc. 144 (2016), 4291-4302 Request permission

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.

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