Details
| Original language | English |
|---|---|
| Pages (from-to) | 1960-1977 |
| Number of pages | 18 |
| Journal | Mathematische Nachrichten |
| Volume | 297 |
| Issue number | 5 |
| Publication status | Published - 11 May 2024 |
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.
Keywords
- Mullins–Sekerka, parabolic smoothing, singular integrals, well-posedness
ASJC Scopus subject areas
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In: Mathematische Nachrichten, Vol. 297, No. 5, 11.05.2024, p. 1960-1977.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The Mullins–Sekerka problem via the method of potentials
AU - Escher, Joachim
AU - Matioc, Anca Voichita
AU - Matioc, Bogdan Vasile
N1 - Publisher Copyright: © 2024 The Authors. Mathematische Nachrichten published by Wiley-VCH GmbH.
PY - 2024/5/11
Y1 - 2024/5/11
N2 - 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.
AB - 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.
KW - Mullins–Sekerka
KW - parabolic smoothing
KW - singular integrals
KW - well-posedness
UR - http://www.scopus.com/inward/record.url?scp=85186426740&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2308.06083
DO - 10.48550/arXiv.2308.06083
M3 - Article
AN - SCOPUS:85186426740
VL - 297
SP - 1960
EP - 1977
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
IS - 5
ER -