Dirichlet Problem at Infinity for $\mathcal A$ -Harmonic Functions

Abstract

We study the Dirichlet problem at infinity for \(\mathcal A\)-harmonic functions on a Cartan–Hadamard manifold M and give a sufficient condition for a point at infinity x0∈M(∞) to be \(\mathcal A\)-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.