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

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