Asymptotically Mean Value Harmonic Functions in Doubling Metric Measure Spaces

Asymptotically Mean Value Harmonic Functions in Doubling Metric Measure Spaces

We consider functions with an asymptotic mean value property, known to characterize harmonicity in Riemannian manifolds and in doubling metric measure spaces. We show that the strongly amv-harmonic functions are Hölder continuous for any exponent below one. More generally, we define the class of fun...

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Bibliographic Details
Main Authors: Adamowicz Tomasz, Kijowski Antoni, Soultanis Elefterios
Format: Article
Language:English
Published: De Gruyter 2022-11-01
Series:Analysis and Geometry in Metric Spaces
Subjects:
asymptotic mean value property
elliptic pdes
harmonic functions
gromov–hausdorff convergence
hölder continuity
mean value property
sobolev spaces
weighted euclidean spaces
primary: 31e05
secondary: 53c23
35r03
Online Access:https://doi.org/10.1515/agms-2022-0143

Internet

https://doi.org/10.1515/agms-2022-0143

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