| Autor: |
Adamowicz Tomasz, Kijowski Antoni, Soultanis Elefterios |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Analysis and Geometry in Metric Spaces, Vol 10, Iss 1, Pp 344-372 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2299-3274 |
| DOI: |
10.1515/agms-2022-0143 |
| Popis: |
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 functions with finite amv-norm and show that functions in this class belong to a fractional Hajłasz–Sobolev space and their blow-ups satisfy the mean-value property. Furthermore, in the weighted Euclidean setting we find an elliptic PDE satisfied by amv-harmonic functions. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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