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.
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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.