Asymptotic Dirichlet problem for the 𝑝-Laplacian on Cartan-Hadamard manifolds

Holopainen, Ilkka

doi:10.1090/S0002-9939-02-06538-3

Asymptotic Dirichlet problem for the $p$-Laplacian on Cartan-Hadamard manifolds
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by Ilkka Holopainen PDF

Proc. Amer. Math. Soc. 130 (2002), 3393-3400 Request permission

Abstract:

We show the existence of nonconstant bounded $p$-harmonic functions on Cartan-Hadamard manifolds of pinched negative curvature by solving the asymptotic Dirichlet problem at infinity for the $p$-Laplacian. More precisely, we prove that given a continuous function $h$ on the sphere at infinity there exists a unique $p$-harmonic function $u$ on $M$ with boundary values $h.$

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