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arXiv · 1312.6285

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

Ilkka Holopainen·Jaime Ripoll
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Abstract

We show, by modifying Borb\'ely's example, that there are $3$-dimen\-sional Cartan-Hadamard manifolds $M$, with sectional curvatures $\le -1$, such that the asymptotic Dirichlet problem for a class of quasilinear elliptic PDEs, including the minimal graph equation, is not solvable.

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Ilkka Holopainen, Jaime Ripoll. 2013-12-21. Nonsolvability of the asymptotic Dirichlet problems for some quasilinear elliptic PDEs on Hadamard manifolds. https://arxiv.org/abs/1312.6285

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