Nonlinear interpolation inequalities with fractional Sobolev norms and pattern formation in biomembranes
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909324352159744 |
|---|---|
| author | Ginster, Janusz Pešić, Anastasija Zwicknagl, Barbara |
| author_facet | Ginster, Janusz Pešić, Anastasija Zwicknagl, Barbara |
| contents | We consider a one-dimensional version of a variational model for pattern formation in biological membranes. The driving term in the energy is a coupling between the order parameter and the local curvature of the membrane. We derive scaling laws for the minimal energy. As a main tool we present new nonlinear interpolation inequalities that bound fractional Sobolev seminorms in terms of a Cahn-Hillard/Modica-Mortola energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16134 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear interpolation inequalities with fractional Sobolev norms and pattern formation in biomembranes Ginster, Janusz Pešić, Anastasija Zwicknagl, Barbara Analysis of PDEs 46E35, 47J20, 49S05, 74K15 We consider a one-dimensional version of a variational model for pattern formation in biological membranes. The driving term in the energy is a coupling between the order parameter and the local curvature of the membrane. We derive scaling laws for the minimal energy. As a main tool we present new nonlinear interpolation inequalities that bound fractional Sobolev seminorms in terms of a Cahn-Hillard/Modica-Mortola energy. |
| title | Nonlinear interpolation inequalities with fractional Sobolev norms and pattern formation in biomembranes |
| topic | Analysis of PDEs 46E35, 47J20, 49S05, 74K15 |
| url | https://arxiv.org/abs/2409.16134 |