Symétrie Des Grandes Solutions D'´ Equations Elliptiques Semi Linéaires Symmetry of Large Solutions of Semilinear Elliptic Equations

Let g : R 7→ R be a locally Lipschitz continuous function and BR(0) the open N -ball (N ≥ 2) of center 0 and radius R > 0. A classical result due to Gidas, Ni and Nirenberg [4] asserts that any positive solution u of (1) −∆u+ g(u) = 0 in BR(0) which vanishes on ∂BR(0) is radial. A conjecture proposed by H. Brezis is that any large solution of (1), that is a solution which verifies (2) lim |x|→R u(x) = ∞,