The Mullins–Sekerka problem via the method of potentials

Joachim Escher; Anca Voichita Matioc; Bogdan Vasile Matioc

doi:10.48550/arXiv.2308.06083

The Mullins–Sekerka problem via the method of potentials

Joachim Escher
, Anca Voichita Matioc
, Bogdan Vasile Matioc^*

^*Corresponding author for this work

Institute of Applied Mathematics

University of Regensburg

Research output: Contribution to journal › Article › Research › peer review

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.

Original language	English
Pages (from-to)	1960-1977
Number of pages	18
Journal	Mathematische Nachrichten
Volume	297
Issue number	5
DOIs	https://doi.org/10.48550/arXiv.2308.06083 https://doi.org/10.1002/mana.202300350
Publication status	Published - 11 May 2024

Keywords

Mullins–Sekerka
parabolic smoothing
singular integrals
well-posedness

ASJC Scopus subject areas

General Mathematics

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10.48550/arXiv.2308.06083Licence: Arxiv nonexclusive-distrib 1.0
10.1002/mana.202300350Licence: CC BY 4.0

Cite this

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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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author = "Joachim Escher and Matioc, \{Anca Voichita\} and Matioc, \{Bogdan Vasile\}",

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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

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The Mullins–Sekerka problem via the method of potentials

Abstract

Keywords

ASJC Scopus subject areas

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