Estimations anisotropes dans les convexes de type fini

Abstract

Let Ω be a smoothly bounded convex domain of finite type m and f be a (0,1)-form ∂ ̄ -closed in Ω. It is proved that the equation ∂ ̄ u=f admits a solution u belonging to the space Λ 1(Ω) (respectively to the anisotropic space Γ α ( ρ) of McNeal–Stein, for all α, 0<α<1/m ) if the anisotropic norm – introduced by Bruna–Charpentier–Dupain – ⦀f⦀ κ,Ω is finite (respectively if the Euclidian norm ‖ f‖ ∞ of the form f is finite).