On the regularity of the interface of a thermodynamically consistent two-phase Stefan problem with surface tension

Abstract

We study the regularity of the free boundary arising in a thermodynamically consistent two-phase Stefan problem with surface tension by means of a family of parameter-dependent diffeomorphisms, $L_p$-maximal regularity theory, and the implicit function theorem.

42 pages

Cited by in corpus (2)

• The Muskat problem in 2D: equivalence of formulations, well-posedness, and regularity results
• Well-posedness of the Muskat problem in subcritical $L_p$-Sobolev spaces