THE BLOW UP LOCUS OF NONLINEAR ELLIPTIC EQUATIONS WITH SUPERCRITICAL EXPONENTS

摘要

Abstract We consider the compactness theorem for the positive solutions of the equation Δu + h_1 u~α + h_2u~β = 0 in Ω in contained in 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‖H~1(Ω)+ ‖u_i‖L~(α+1)(Ω) 　+ ‖u_i‖L~(β+1)(Ω)} bounded.