Robin Green Function Estimates and a Model of Mammalian Lungs
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909693243293696 |
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| author | David, Guy Decio, Stefano Engelstein, Max Filoche, Marcel Mayboroda, Svitlana Michetti, Marco |
| author_facet | David, Guy Decio, Stefano Engelstein, Max Filoche, Marcel Mayboroda, Svitlana Michetti, Marco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robin Green Function Estimates and a Model of Mammalian Lungs David, Guy Decio, Stefano Engelstein, Max Filoche, Marcel Mayboroda, Svitlana Michetti, Marco Analysis of PDEs Classical Analysis and ODEs 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. |
| title | Robin Green Function Estimates and a Model of Mammalian Lungs |
| topic | Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2507.13168 |