Potential Analysis

, Volume 48, Issue 3, pp 325–335 | Cite as

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.


Singular PDEs Regularity theory 

Mathematics Subject Classification (2010)

35B65 35J60 


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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.University of Central FloridaOrlandoUSA

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