https://hal-enpc.archives-ouvertes.fr/hal-00779545Pacard, F.F.PacardCERGRENE - CERGRENE - ENGREF - Ecole Nationale du Génie Rural, des Eaux et des Forêts - ENPC - École des Ponts ParisTechPartial regularity for weak solutions of a nonlinear elliptic equationHAL CCSD1993[SDE] Environmental SciencesEnpc, Ist2013-01-22 13:11:562022-11-04 14:38:292013-01-22 13:11:56enJournal articles10.1007/BF025683351For 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.