The Mullins–Sekerka problem via the method of potentials

URN to cite this document:: urn:nbn:de:bvb:355-epub-555935
DOI to cite this document:: 10.5283/epub.55593

Escher, Joachim ; Matioc, Anca‐Voichita ; Matioc, Bogdan‐Vasile

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Date of publication of this fulltext: 27 Feb 2024 06:40

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Abstract

It is shown that the two-dimensional Mullins–Sekerka problem is well-posed in all subcritical Sobolev spaces with . 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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