JournalsrmiVol. 31, No. 3pp. 1107–1129

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

  • Ilkka Holopainen

    University of Helsinki, Finland

  • Jaime B. Ripoll

    Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil
Nonsolvability of the asymptotic Dirichlet problem for some quasilinear elliptic PDEs on Hadamard manifolds cover
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Abstract

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. 1107–1129

DOI 10.4171/RMI/864