The Mullins–Sekerka problem via the method of potentials

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OriginalspracheEnglisch
Seiten (von - bis)1960-1977
Seitenumfang18
FachzeitschriftMathematische Nachrichten
Jahrgang297
Ausgabenummer5
PublikationsstatusVeröffentlicht - 11 Mai 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.

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The Mullins–Sekerka problem via the method of potentials. / Escher, Joachim; Matioc, Anca Voichita; Matioc, Bogdan Vasile.
in: Mathematische Nachrichten, Jahrgang 297, Nr. 5, 11.05.2024, S. 1960-1977.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Escher J, Matioc AV, Matioc BV. The Mullins–Sekerka problem via the method of potentials. Mathematische Nachrichten. 2024 Mai 11;297(5):1960-1977. doi: 10.48550/arXiv.2308.06083, 10.1002/mana.202300350
Escher, Joachim ; Matioc, Anca Voichita ; Matioc, Bogdan Vasile. / The Mullins–Sekerka problem via the method of potentials. in: Mathematische Nachrichten. 2024 ; Jahrgang 297, Nr. 5. S. 1960-1977.
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