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

Abstract

We show, by modifying Borbély's 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.

arXiv admin note: text overlap with arXiv:1311.5693

References in corpus (2)

• The half-space property and entire positive minimal graphs in M x R
• On the asymptotic Dirichlet problem for the minimal hypersurface equation in a Hadamard manifold

Cited by in corpus (4)

• Convexity at infinity in Cartan-Hadamard manifolds and applications to the asymptotic Dirichlet and Plateau problems
• Survey on the asymptotic Dirichlet problem for the minimal surface equation
• On the asymptotic Dirichlet problem for the minimal hypersurface equation in a Hadamard manifold
• Some existence results to the Dirichlet problem for the minimal hypersurface equation on non mean convex domains of a Riemannian manifold