The Mullins–Sekerka problem via the method of potentials

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

Mathematische Nachrichten, 2024, vol. 297, issue 5, 1960-1977

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∈(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.

Date: 2024
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