Uniform bounds for quotients of Green functions on C 1 , 1 -domains
Hermann Hueber, Malte Sieveking · Annales de l’institut Fourier · 1982
Let Δ u = Σ i ∂ 2 ∂ x i 2 , L u = Σ i , j a i j ∂ 2 ∂ x i ∂ x j u + Σ i b i ∂ ∂ x i u + c u be elliptic operators with Hölder continuous coefficients on a bounded domain Ω ⊂ R n of class C 1 , 1 . There is a constant c > 0 depending only on the Hölder norms of the coefficients of L and its constant of ellipticity such that c - 1 G Δ Ω ≤ G L Ω ≤ c G Δ Ω on Ω × Ω , where γ Δ Ω (resp. G L Ω ) are the Green functions of Δ (resp. L ) on Ω .