Robin Green Function Estimates and a Model of Mammalian Lungs
Analysis of PDEs
2025-07-18 v1 Classical Analysis and ODEs
Abstract
The present paper establishes delicate properties of the Green function with Robin boundary conditions, in particular, elucidating the nature of the passage between the Dirichlet-like and Neumann-like behavior. This yields sharp quantifiable bounds on the corresponding harmonic measure and proves the phase transition in the behavior of the total flow earlier conjectured in physics literature in concert with the efficacy of mammalian lungs.
Cite
@article{arxiv.2507.13168,
title = {Robin Green Function Estimates and a Model of Mammalian Lungs},
author = {Guy David and Stefano Decio and Max Engelstein and Marcel Filoche and Svitlana Mayboroda and Marco Michetti},
journal= {arXiv preprint arXiv:2507.13168},
year = {2025}
}
Comments
56 pages. Comments welcome!