Lipschitz Continuity for Elliptic Free Boundary Problems with Dini Mean Oscillation Coefficients
Abstract
We establish local interior Lipschitz continuity of the solutions of a class of free boundary elliptic problems assuming the coefficients of the equation of Dini mean oscillation in at least one direction. The novelty in this regularity result lies in the fact that it allows discontinuous coefficients in all but one variable.
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