The Blow Up Locus of Nonlinear Elliptic Equations with Supercritical Exponents

Abstract

We consider the compactness theorem for the positive solutions of the equation Δu + h_1u^α + h_2u^β = 0 in Ω ⊂ R^n and obtain the measure estimate of the blow up set for positive smooth solutions {u_i} of the above equation with {||u_i||_{H¹(Ω)} + ||u_i||_{L^{α+1}(Ω)} + ||u_i||_L^{β+1}(Ω)} bounded.