Nonlinear Elliptic Equations With Mixed Singularities

We study non-variational degenerate elliptic equations with mixed singular structures, both at the set of critical points and on the ground touching points. No boundary data are imposed and singularities occur along an a priori unknown interior region. We prove that positive solutions have a universal modulus of continuity that does not depend on their infimum value. We further obtain sharp, quantitative regularity estimates for non-negative limiting solutions