Bounding Radial Variation of positive harmonic Functions on Lipschitz Domains
Jakob Fromherz, Paul F.X. M\"uller, Katharina Riegler
TL;DR
This paper refines radial variation estimates for positive harmonic functions on Lipschitz domains, improving previous proofs and extending understanding in higher dimensions.
Contribution
It provides an updated, more precise proof of radial variation bounds for harmonic functions on Lipschitz domains, enhancing prior results.
Findings
Refined radial variation estimates for harmonic functions
Modified proof of Mozolyako and Havin for Lipschitz domains
Extension of results to higher dimensions
Abstract
We provide radial variational estimates for positive harmonic functions on Lipschitz domains in higher dimensions. The intention of this paper is to document an updated and refined version of arXiv:2003.07176 which modifies the proof of Mozolyako and Havin for Lipschitz domains.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Numerical methods in inverse problems · Nonlinear Partial Differential Equations