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

DOI10.4171/RMI/864zbMath1330.58017arXiv1312.6285MaRDI QIDQ888931

Ilkka Holopainen, Jaime Bruck Ripoll

Publication date: 3 November 2015

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.6285

zbMATH Keywords

Dirichlet problemHadamard manifoldminimal graph equationquasilinear elliptic partial differential equations

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Boundary value problems on manifolds (58J32) Other generalizations (nonlinear potential theory, etc.) (31C45) Quasilinear elliptic equations (35J62)

Related Items

The Dirichlet problem for the minimal hypersurface equation on arbitrary domains of a Riemannian manifold, Recent rigidity results for graphs with prescribed mean curvature, On the asymptotic Dirichlet problem for the minimal hypersurface equation in a Hadamard manifold, Convexity at infinity in Cartan-Hadamard manifolds and applications to the asymptotic Dirichlet and Plateau problems, Solvability of minimal graph equation under pointwise pinching condition for sectional curvatures, Existence and non-existence of minimal graphic and p-harmonic functions, Survey on the asymptotic Dirichlet problem for the minimal surface equation, Regularity at infinity of Hadamard manifolds with respect to some elliptic operators and applications to asymptotic Dirichlet problems

Cites Work

• Negatively curved manifolds, elliptic operators, and the Martin boundary
• Unnamed Item