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High-frequency estimates for the Neumann scattering phase in non-smooth obstacle scattering

In this paper the high-frequency asymptotics of the Neumann scattering phase s(λ) in acoustic obstacle scattering is considered. Under certain conditions it is proved that if the boundary ∂Γ of an obstacle Γ has finite upper δ-Minkowski content µ*(δ,∂Γ), then there is a positive constant Cn,δ, depending only on n and δ, such that and as λ→∞, where wn is the volume of the unit ball in ℝn.