Nonlinear elliptic equations with high order singularities

Abstract

We study non-variational degenerate elliptic equations with high order singular structures. No boundary data are imposed and singularities occur along an {\it 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.

Revised

References in corpus (1)

• $C^{1,\alpha }$ regularity of solutions of degenerate fully non-linear elliptic equations

Cited by in corpus (1)

• Infinity Laplacian equations with singular absorptions