Half-space solutions with $7/2$ frequency in the thin obstacle problem

Abstract

For the thin obstacle problem in 3d, we show that half-space solutions form an isolated family in the space of $7/2$-homogeneous solutions. For a general solution with one blow-up profile in this family, we establish the rate of convergence to this profile. As a consequence, we obtain regularity of the free boundary near such contact points.

arXiv comment64 pages with 4 figures

References in corpus (4)

• Some New Monotonicity Formulas and the Singular Set in the Lower Dimensional Obstacle Problem
• Direct epiperimetric inequalities for the thin obstacle problem and applications
• On the measure and the structure of the free boundary of the lower dimensional obstacle problem
• Free boundary regularity in the triple membrane problem

Cited by in corpus (2)

• Free boundary partial regularity in the thin obstacle problem
• Free boundary regularity in the multiple membrane problem in the plane