• Citer

On the Asymptotic Dirichlet Problem for the Minimal Hypersurface Equation in a Hadamard Manifold

par Casteras, Jean-Baptiste ;Holopainen, Ilkka;Ripoll, Jaime Bruck
Référence Potential analysis, 47, 4, page (485-501)
Publication Publié, 2017-11

Article révisé par les pairs

• Détails
• Contenu

Résumé :

We study the Dirichlet problem at infinity on a Cartan-Hadamard manifold M of dimension n ≥ 2 for a large class of operators containing, in particular, the p-Laplacian and the minimal graph operator. We extend several existence results obtained for the p-Laplacian to our class of operators. As an application of our main result, we prove the solvability of the asymptotic Dirichlet problem for the minimal graph equation for any continuous boundary data on a (possibly non rotationally symmetric) manifold whose sectional curvatures are allowed to decay to 0 quadratically.