Oscillatory free boundary problems in heterogeneous media

Abstract

We investigate a class of free boundary problems with oscillatory singularities within heterogeneous media. Our main result yields sharp regularity estimates along the free boundary, provided the power of the singularity varies in a Dini-continuous fashion below a certain threshold. We also reveal an interesting repelling estimate preventing the free boundary from touching the region where the singularity power oscillates above the threshold.

arXiv commentTo appear in the J. London Math. Soc