Escher, Joachim and Matioc, Anca-Voichita and Matioc, Bogdan-Vasile (2024) The Mullins-Sekerka problem via the method of potentials. MATHEMATISCHE NACHRICHTEN, 297 (5). pp. 1960-1977. ISSN 0025-584X, 1522-2616
Full text not available from this repository. (Request a copy)Abstract
It is shown that the two-dimensional Mullins-Sekerka problem is well-posed in all subcritical Sobolev spaces Hr(R)$H<^>r({\mathbb {R}})$ with r is an element of(3/2,2)$r\in (3/2,2)$. 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CAHN-HILLIARD EQUATION; CLASSICAL-SOLUTIONS; WEAK SOLUTIONS; MUSKAT PROBLEM; REGULARITY; INTERFACE; CONVERGENCE; EXISTENCE; Mullins-Sekerka; parabolic smoothing; singular integrals; well-posedness |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 16 Jul 2025 06:53 |
| Last Modified: | 16 Jul 2025 06:53 |
| URI: | https://pred.uni-regensburg.de/id/eprint/63528 |
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