Partial regularity for minimizing constraint maps for the Alt-Phillips energy

TL;DR

This paper proves an epsilon-regularity theorem for minimizers of an Alt-Phillips energy functional with constraints, demonstrating that small energy implies smoothness and leading to optimal regularity results.

Contribution

The authors establish a new epsilon-regularity theorem for constrained minimizers of the Alt-Phillips energy, advancing understanding of their regularity properties.

Findings

Small energy implies regularity of minimizers.

Minimizers are smooth under certain energy conditions.

Achieves optimal regularity through bootstrap arguments.

Abstract

In this paper, we establish an $\varepsilon$-regularity theorem for minimizers of an Alt-Phillips type functional subject to constraint maps. We prove that under sufficiently small energy, the minimizers exhibit regularity, and hence proving the smoothness of these maps. From here, we bootstrap to optimal regularity.