Concentration of cones in the Alt-Phillips problem

Abstract

We study minimizing cones in the Alt-Phillips problem when the exponent γ is close to 1. When γ converges to 1, we show that the cones concentrate around symmetric solutions to the classical obstacle problem. To be precise, the limiting profiles are radial in a subspace and invariant in directions perpendicular to that subspace.

Updated the list of references. To appear in ARMA