English

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.

Keywords

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!