IUMJ

Title: The growth of the Martin kernel in a horn-shaped domain

Authors: Dante DeBlassie

Issue: Volume 57 (2008), Issue 7, 3115-3130

Abstract:

If a horn-shaped domain in $\mathbb{R}^{d+1}$ does not open too rapidly at $\infty$, then the Martin boundary (with respect to the Laplacian) at $\infty$ is homeomorphic to the sphere $S^{d-1}$. Given a point $\varphi$ in the sphere, we determine the growth rate of the Martin kernel with pole at $\varphi$ explicitly in terms of the speed at which the horn opens at $\infty$.