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We prove optimal regularity for the double obstacle problem when obstaclesare given by solutions to Hamilton-Jacobi equations that are not $C^2$.  When the Hamilton-Jacobi equation is not $C^2$ then the standard Bernsteintechnique fails and we loose the usual semi-concavity estimates. Using anon-homogeneous scaling (different speed in different directions) we develop anew pointwise regularity theory for Hamilton-Jacobi equations at points wherethe solution touches the obstacle.  A consequence of our result is that $C^1$-solutions to the Hamilton-Jacobiequation $$ \pm |\nabla h-a(x)|^2=\pm 1 \textrm{in} B_1, \qquad h=f \textrm{on}\partial B_1, $$ are in fact $C^{1,\alpha/2}$ provided that $a \in C^\alpha$.This result is optimal and to the authors' best knowledge new.

Double Obstacle Problems with obstacles given by non-$C^2$ Hamilton-Jacobi equations