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

2013/12/21 by Ilkka Holopainen, Jaime Ripoll, Holopainen, Ilkka +1
Mathematics · #31C45 #53C21 #58J32 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:31C45 #msc:53C21 #msc:58J32

paper · pdf · doi:10.48550/arxiv.1312.6285

arXiv admin note: text overlap with arXiv:1311.5693

arxiv created 2013/12/21 · arxiv updated 2013/12/24

Abstract

We show, by modifying Borbély's example, that there are 3-dimen\-sional 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.

Citations

• On the asymptotic Dirichlet problem for the minimal hypersurface equation in a Hadamard manifold

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