Asymptotic Dirichlet Problem for $mathcal {A}$-Harmonic Functions on Manifolds with Pinched Curvature

We study the asymptotic Dirichlet problem for (mathcal {A})-harmonic functions on a Cartan-Hadamard manifold whose radial sectional curvatures outside a compact set satisfy an upper bound ( K(P)le - frac {1+varepsilon }{r(x)^{2} log r(x)} ) and a pointwise pinching condition ( | K(P) |le C_{K}| K(P^{prime }) | ) for some constants ε > 0 and C _K ≥ 1, where P and (P^{prime }) are any 2-dimensional subspaces of T _x M containing the (radial) vector ?r(x) and r(x) = d(o, x) is the distance to a fixed point o ∈ M. We solve the asymptotic Dirichlet problem with any continuous boundary data (fin C(partial _{infty } M)). The results apply also to the Laplacian and p-Laplacian, (1 as special cases.