Abstract
For a strictly convex set K⊂R2 of class C2 we consider its associated sub-Finsler K-perimeter |∂E|K in H1 and the prescribed mean curvature functional |∂E|K−∫Ef associated to a continuous function f. Given a critical set for this functional with Euclidean Lipschitz and intrinsic regular boundary, we prove that their characteristic curves are of class C2 and that this regularity is optimal. The result holds in particular when the boundary of E is of class C1.
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