Asymptotic Dirichlet problem for A-harmonic and minimal graph equations in Cartan-Hadamard manifolds

We study the asymptotic Dirichlet problem for A-harmonic equations and for the minimal graph equation on a Cartan-Hadamard manifold M whose sectional curvatures are bounded from below and above by certain functions depending on the distance to a fixed point in M. We are, in particular, interested in finding optimal (or close to optimal) curvature upper bounds.

Nonsolvability of the asymptotic Dirichlet problems for some quasilinear elliptic PDEs on Hadamard manifolds

We show, by modifying Borbelys example, that there are $3$-dimen-sional Cartan-Hadamard manifolds $M$, with sectional curvatures $le -1$, such that the asymptotic Dirichlet problem for a class of quasilinear elliptic PDEs, including the minimal graph equation, is not solvable.

On the asymptotic Dirichlet problem for the minimal hypersurface equation in a Hadamard manifold

We study the Dirichlet problem at infinity on a Cartan-Hadamard manifold for a large class of operators containing in particular the p-Laplacian and the minimal graph operator.