For stationary solutions of Δu=u^{-p}+f, the rupture set {u=0} is (n-2)-rectifiable with a sharp Minkowski-type estimate, and derivatives satisfy optimal Lorentz integrability.
Alper, Rectifiability of line defects in liquid crysta ls with variable degree of orientation, Archive for Rational Mechanics and Analysis , 228 (2018), 309-339
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Fine structure of rupture set for semilinear elliptic equation with singular nonlinearity
For stationary solutions of Δu=u^{-p}+f, the rupture set {u=0} is (n-2)-rectifiable with a sharp Minkowski-type estimate, and derivatives satisfy optimal Lorentz integrability.