For a wide class of compact connected C2 curves Pi without rank-one connections but non-elliptic, Du is locally Lipschitz outside a discrete set with rigid characterization at singularities; no singularities hold under partial ellipticity or topological restrictions on the tangent bundle.
Kinetic formulation of conservation laws , volume 21 of Oxf
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On regularity and rigidity of $2\times 2$ differential inclusions into non-elliptic curves
For a wide class of compact connected C2 curves Pi without rank-one connections but non-elliptic, Du is locally Lipschitz outside a discrete set with rigid characterization at singularities; no singularities hold under partial ellipticity or topological restrictions on the tangent bundle.