Partial regularity for weak solutions of a nonlinear elliptic equation

F. Pacard (1)

1 CERGRENE - CERGRENE

For scalar non-linear elliptic equations, stationary solutions are defined to be critical points of a functional with respect to the variations of the domain. We consider u a weak positive solution of -Δu=uα in -Δu=uα in Ω ⊂ ℝn, which is stationary. We prove that the Hausdorff dimension of the singular set of u is less than n-2α+1/α-1, if α≥n+2/n-2. © 1993 Springer-Verlag.

Domains: Environmental Sciences

F. Pacard. Partial regularity for weak solutions of a nonlinear elliptic equation. Manuscripta mathematica, 1993, 79 (1), pp.161. ⟨10.1007/BF02568335⟩. ⟨hal-00779545⟩