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- W2154398857 abstract "In this note we consider a stability property of p-harmonic functions in general metric measure spaces. Despite the fact that there may not be a corresponding differential equation, it is shown here that a family of uniformly convergent p-harmonic functions converges to a p-harmonic function; that is, the collection of p-harmonic functions forms a closed subspace in a certain Hölder class. As a consequence, it is shown that a family of p-harmonic functions bounded in a Sobolev-type space (called the Newtonian space) has a sequence that converges locally uniformly in the domain of harmonicity to a p-harmonic function. This result is used to construct p-harmonic functions on unbounded domains. We also use this convergence result to prove a characterization of a parabolicity property of metric measure spaces. This characterization has been given for Riemannian manifolds by Holopainen, and the result here is a generalization of Holopainen's result. 2000 Mathematics Subject Classification 31C05 (primary), 31C45, 30C99 (secondary)" @default.
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- W2154398857 date "2003-06-25" @default.
- W2154398857 modified "2023-09-27" @default.
- W2154398857 title "Some Convergence Results for p-Harmonic Functions on Metric Measure Spaces" @default.
- W2154398857 doi "https://doi.org/10.1112/s0024611503014151" @default.
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