Dirichlet Problem at Infinity for $\mathcal A$-Harmonic Functions |
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Authors: | Aleksi Vähäkangas |
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Institution: | 1.Department of Mathematics and Statistics,University of Helsinki,Helsinki,Finland |
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Abstract: | We study the Dirichlet problem at infinity for -harmonic functions on a Cartan–Hadamard manifold M and give a sufficient condition for a point at infinity x
0∈M(∞) to be -regular. This condition is local in the sense that it only involves sectional curvatures of M in a set U∩M, where U is an arbitrary neighborhood of x
0 in the cone topology. The results apply to the Laplacian and p-Laplacian, 1<p<∞, as special cases.
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Keywords: | Cartan– Hadamard manifold ![](/content/03t6516552051mvj/11118_2007_9051_Article_IEq4) -harmonic function" target="_blank">gif" alt="$\mathcal A$" align="middle" border="0">-harmonic function Dirichlet problem |
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