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arXiv · 1304.1681

The Dirichlet problem for p-harmonic functions on the topologist's comb

Anders Björn
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Abstract

In this paper we study the Perron method for solving the p-harmonic Dirichlet problem on the topologist's comb. For functions which are bounded and continuous at the accessible points, we obtain invariance of the Perron solutions under arbitrary perturbations on the set of inaccessible points. We also obtain some results allowing for jumps and perturbations at a countable set of points.

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Anders Björn. 2013-04-05. The Dirichlet problem for p-harmonic functions on the topologist's comb. https://doi.org/10.1007/s00209-014-1373-8

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