BOUNDEDNESS OF THE EXTREMAL SOLUTION FOR SEMILINEAR ELLIPTIC PROBLEMS
Dong Ye, Feng Zhou · Communications in Contemporary Mathematics · 2002
We investigate here the boundedness of extremal solutions for some semilinear elliptic equation -Δu=λf(u) posed on a bounded smooth domain of ℝN with Dirichlet boundary condition. Some sufficient conditions for f are established to ensure the regularity of extremal solutions when N ≤ 9, which cover all well-known cases.