Boundary behavior of p-harmonic functions in the Heisenberg group
Document Type
Article
Publication Date
11-1-2011
Abstract
In this paper we study the boundary behavior of nonnegative p-harmonic functions in a bounded domain in the Heisenberg group ℍn. Under suitable geometric assumptions on the ground domain Ω ⊂ ℍn our main contributions can be summarized as follows: (1) In Theorem 1.1 we obtain an estimate from above stating that any such function should vanish at most linearly like the sub-Riemannian distance from the boundary:, where Ar(g0) ∈ Ω is a non-tangential point relative to (g0) ∈ ∂Ω. (2) In Theorem 1.2 we establish an estimate from below which states that, away from the characteristic set of Ω, the order of vanishing is exactly linear, i. e.:,. © 2010 Springer-Verlag.
Publication Source (Journal or Book title)
Mathematische Annalen
First Page
587
Last Page
632
Recommended Citation
Garofalo, N., & Phuc, N. (2011). Boundary behavior of p-harmonic functions in the Heisenberg group. Mathematische Annalen, 351 (3), 587-632. https://doi.org/10.1007/s00208-010-0611-6