Ein Beitrag zur Lipschitz-Saturation im unendlichdimensionalen Fall
Let f: ℝⁿ → ℝ be a polynomial function of degree d with f(0) = 0 and ∇f(0) = 0. Łojasiewicz’s gradient inequality states that there exist C > 0 and ϱ ∈ (0,1) such that in a neighbourhood of the origin. We prove that the smallest such exponent ϱ is not greater than with .