Revista Matemática Iberoamericana
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Published online: 2015-10-29
Nonsolvability of the asymptotic Dirichlet problem for some quasilinear elliptic PDEs on Hadamard manifoldsIlkka Holopainen and Jaime B. Ripoll (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. Iberoam. 31 (2015), 1107-1129. doi: 10.4171/RMI/864