For suitable harmonic map flows, every time slice of the singular set is (n-2)-rectifiable with uniform Minkowski content estimates, and excluding harmonic and quasi-harmonic 2-spheres yields a sharp L^{3,∞} bound on the gradient.
Chang, Heat flow and boundary value problem for harmonic maps,Annales de l’Institut Henri Poincar´ e C, Analyse non lineaire,6(1989), 363-395
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Stratification and rectifiability of harmonic map flows via tangent measures
For suitable harmonic map flows, every time slice of the singular set is (n-2)-rectifiable with uniform Minkowski content estimates, and excluding harmonic and quasi-harmonic 2-spheres yields a sharp L^{3,∞} bound on the gradient.