We show, by modifying Borbély’s example, that there are 3-dimensional Cartan–Hadamard manifolds , 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.
Cite this article
Ilkka Holopainen, Jaime B. Ripoll, Nonsolvability of the asymptotic Dirichlet problem for some quasilinear elliptic PDEs on Hadamard manifolds. Rev. Mat. Iberoam. 31 (2015), no. 3, pp. 1107–1129DOI 10.4171/RMI/864