Revista Matemática Iberoamericana


Full-Text PDF (331 KB) | Metadata | Table of Contents | RMI summary
Volume 31, Issue 3, 2015, pp. 1107–1129
DOI: 10.4171/RMI/864

Published online: 2015-10-29

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

Ilkka Holopainen[1] and Jaime B. Ripoll[2]

(1) University of Helsinki, Finland
(2) Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil

We show, by modifying Borbély’s example, that there are 3-dimensional Cartan–Hadamard manifolds $M$, with sectional curvatures ≤ −1, such that the asymptotic Dirichlet problem for a class of quasilinear elliptic PDEs, including the minimal graph equation, is not solvable.

Keywords: Minimal graph equation, Dirichlet problem, Hadamard manifold

Holopainen Ilkka, Ripoll Jaime: Nonsolvability of the asymptotic Dirichlet problem for some quasilinear elliptic PDEs on Hadamard manifolds. Rev. Mat. Iberoamericana 31 (2015), 1107-1129. doi: 10.4171/RMI/864