Boundary Harnack estimates in slit domains and applications to thin free boundary problems

Abstract

We provide a higher order boundary Harnack inequality for harmonic functions in slit domains. As a corollary we obtain the $C^{\infty }$ regularity of the free boundary in the Signorini problem near non-degenerate points.

Cited by in corpus (1)

• Higher regularity of the free boundary in the elliptic Signorini problem