Regularity of the free boundary for two-phase problems governed by divergence form equations and applications

Abstract

We study a class of two-phase inhomogeneous free boundary problems governed by elliptic equations in divergence form. In particular we prove that Lipschitz or flat free boundaries are $C^{1,\gamma }$. Our results apply to the classical Prandtl-Bachelor model in fluiddynamics.

28 pages. arXiv admin note: text overlap with arXiv:1210.7226, arXiv:1304.0406

References in corpus (1)

• Two-phase problems with distributed source: regularity of the free boundary

Cited by in corpus (2)

• The free boundary of steady axisymmetric inviscid flow with vorticity II: near the non-degenerate points
• An epiperimetric inequality for the regularity of some free boundary problems: the $2$-dimensional case