Reifenberg Flatness of Free Boundaries in Obstacle Problems with VMO Ingredients
arXiv:1309.3077
Abstract
We study the obstacle problem with an elliptic operator in divergence form. We develop all of the basic theory of existence, uniqueness, optimal regularity, and nondegeneracy of the solutions. These results, in turn, allow us to begin the study of the regularity of the free boundary in the case where the coefficients are in VMO.
arXiv comment22 pages. No figures. Very minor revisions to previous version. Improvement of exposition and addition of definition of "relatively Reifenberg vanishing."