Uniform $C^{1,\alpha }$-regularity for almost-minimizers of some nonlocal perturbations of the perimeter

Michael Goldman, Benoît Merlet, Marc Pegon

In this paper, we establish a $C^{1,\alpha }$-regularity theorem for almost-minimizers of the functional ${\mathcal{F}}_{\epsilon ,\gamma }=P-\gamma P_{\epsilon }$, where $\gamma \in (0,1)$ and $P_{\vare…