On the non-tangential touch between the free and the fixed boundaries for the two-phase obstacle-like problem

Abstract

Abstract. In this paper we consider the following two-phase obstacleproblem-like equation in the unit half-ballWe classify the angles of touch between the free boundary and the fixed one if the boundary data f satisfies certain conditions. This results are connected to the results from [AMM].

Boundary Regularity and Nontransversal Intersection for the Fully Nonlinear Obstacle Problem

“…If this is not the case, the free boundary may approach the fixed boundary at an angle [2]. Several variations of the classical tangential touch problem in recent years have appeared in [3,[5][6][7]20]. It is of interest to study the largest function space for which uniform results hold.…”