Infinity Laplacian equations with singular absorptions

Sharp regularity for singular obstacle problems

“…The problem (1.1) was studied in [21] (with p = 2 and flat obstacle), where, using a minimizer preserving scaling, it was shown that minimizers are locally of the class C 1, γ 2−γ , 0 < γ < 1 (see also [4] and [5], for the problem governed by the infinity Laplacian and uniformly elliptic fully nonlinear operators, respectively). There are, so called, monotonicity formulas available in the linear case, which play a crucial role in the study of the problem.…”