A Notion of Rectifiability Modeled on Carnot Groups

Gary Lieberman, Regularity of Solutions to Some Degenerate Double Obstacle Problems, Indiana Univ. Math. J. 40 (1991), 1009-1028

Abstract

We study double obstacle problems for a class of elliptic operators modelled on the $p$ -Laplacian operator: $Qu = \operatorname{div}(| {Du} |_{P - 2} Du)$ for $p > 1$ . When the obstacles are $C^{1,\alpha }$ (with $\alpha$ sufficiently small), so is the solution; this regularity is proved both locally and up to the boundary.

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