Nonlinear elliptic equations with high order singularities

الأصل · EN

We study non-variational degenerate elliptic equations with high order singular structures. 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.