Phase separation on varying surfaces and convergence of diffuse interface approximations
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910565220220928 |
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| author | Olbermann, Heiner Röger, Matthias |
| author_facet | Olbermann, Heiner Röger, Matthias |
| contents | In this paper we consider phase separations on (generalized) hypersurfaces in Euclidian space. We consider a diffuse surface area (line tension) energy of Modica-Mortola type and prove a compactness and lower bound estimate in the sharp interface limit. We use the concept of generalized BV functions over currents as introduced by Anzellotti et. al. [Annali di Matematica Pura ed Applicata, 170, 1996] to give a suitable formulation in the limit and achieve the necessary compactness property. We also consider an application to phase separated biomembranes where a Willmore energy for the membranes is combined with a generalized line tension energy. For a diffuse description of such energies we give a lower bound estimate in the sharp interface limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01865 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Phase separation on varying surfaces and convergence of diffuse interface approximations Olbermann, Heiner Röger, Matthias Analysis of PDEs 49Q20, 49J45, 92C10 In this paper we consider phase separations on (generalized) hypersurfaces in Euclidian space. We consider a diffuse surface area (line tension) energy of Modica-Mortola type and prove a compactness and lower bound estimate in the sharp interface limit. We use the concept of generalized BV functions over currents as introduced by Anzellotti et. al. [Annali di Matematica Pura ed Applicata, 170, 1996] to give a suitable formulation in the limit and achieve the necessary compactness property. We also consider an application to phase separated biomembranes where a Willmore energy for the membranes is combined with a generalized line tension energy. For a diffuse description of such energies we give a lower bound estimate in the sharp interface limit. |
| title | Phase separation on varying surfaces and convergence of diffuse interface approximations |
| topic | Analysis of PDEs 49Q20, 49J45, 92C10 |
| url | https://arxiv.org/abs/2307.01865 |