A1 Journal article (refereed)
Volume growth, capacity estimates, p-parabolicity and sharp integrability properties of p-harmonic Green functions (2023)


Björn, A., Björn, J., & Lehrbäck, J. (2023). Volume growth, capacity estimates, p-parabolicity and sharp integrability properties of p-harmonic Green functions. Journal d'Analyse Mathematique, 150(1), 159-214. https://doi.org/10.1007/s11854-023-0273-4


JYU authors or editors


Publication details

All authors or editors: Björn, Anders; Björn, Jana; Lehrbäck, Juha

Journal or series: Journal d'Analyse Mathematique

ISSN: 0021-7670

eISSN: 1565-8538

Publication year: 2023

Publication date: 20/03/2023

Volume: 150

Issue number: 1

Pages range: 159-214

Publisher: Hebrew University Magnes Press; Springer

Publication country: Israel

Publication language: English

DOI: https://doi.org/10.1007/s11854-023-0273-4

Publication open access: Not open

Publication channel open access: 

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/93700

Web address of parallel published publication (pre-print): https://arxiv.org/pdf/2101.11486.pdf


Abstract

In a complete metric space equipped with a doubling measure supporting a p-Poincaré inequality, we prove sharp growth and integrability results for p-harmonic Green functions and their minimal p-weak upper gradients. We show that these properties are determined by the growth of the underlying measure near the singularity. Corresponding results are obtained also for more general p-harmonic functions with poles, as well as for singular solutions of elliptic differential equations in divergence form on weighted Rn and on manifolds.

The proofs are based on a new general capacity estimate for annuli, which implies precise pointwise estimates for p-harmonic Green functions. The capacity estimate is valid under considerably milder assumptions than above. We also use it, under these milder assumptions, to characterize singletons of zero capacity and the p-parabolicity of the space. This generalizes and improves earlier results that have been important especially in the context of Riemannian manifolds.


Keywords: potential theory; measure theory; metric spaces; Riemannian manifolds


Contributing organizations


Ministry reporting: Yes

Reporting Year: 2023

Preliminary JUFO rating: 2


Last updated on 2024-03-04 at 19:25