The Mullins–Sekerka problem via the method of potentials
- authored by
- Joachim Escher, Anca Voichita Matioc, Bogdan Vasile Matioc
- Abstract
It is shown that the two-dimensional Mullins–Sekerka problem is well-posed in all subcritical Sobolev spaces (Formula presented.) with (Formula presented.). This is the first result, where this issue is established in an unbounded geometry. The novelty of our approach is the use of the potential theory to formulate the model as an evolution problem with nonlinearities expressed by singular integral operators.
- Organisation(s)
-
Institute of Applied Mathematics
- External Organisation(s)
-
University of Regensburg
- Type
- Article
- Journal
- Mathematische Nachrichten
- Volume
- 297
- Pages
- 1960-1977
- No. of pages
- 18
- ISSN
- 0025-584X
- Publication date
- 11.05.2024
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- General Mathematics
- Electronic version(s)
-
https://doi.org/10.48550/arXiv.2308.06083 (Access:
Open)
https://doi.org/10.1002/mana.202300350 (Access: Open)
