%0 Journal Article
%T Regularity of the extremal solution for some elliptic problems with advection
%A Xue Luo
%A Dong Ye
%A Feng Zhou
%J Mathematics
%D 2010
%I arXiv
%X In this note, we investigate the regularity of extremal solution $u^*$ for semilinear elliptic equation $-\triangle u+c(x)\cdot\nabla u=\lambda f(u)$ on a bounded smooth domain of $\mathbb{R}^n$ with Dirichlet boundary condition. Here $f$ is a positive nondecreasing convex function, exploding at a finite value $a\in (0, \infty)$. We show that the extremal solution is regular in low dimensional case. In particular, we prove that for the radial case, all extremal solution is regular in dimension two.
%U http://arxiv.org/abs/1004.3956v2