Dirichlet Problem at Infinity for $mathcal A$-Harmonic Functions
Authors:
Aleksi Vähäkangas
Affiliation:
1.Department of Mathematics and Statistics,University of Helsinki,Helsinki,Finland
Abstract:
We study the Dirichlet problem at infinity for -harmonic functions on a Cartan–Hadamard manifold M and give a sufficient condition for a point at infinity x0∈M(∞) to be -regular. This condition is local in the sense that it only involves sectional curvatures of M in a set U∩M, where U is an arbitrary neighborhood of x0 in the cone topology. The results apply to the Laplacian and p-Laplacian, 1<p<∞, as special cases.