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

In this paper the high-frequency asymptotics of the Neumann scattering phas e s (lambda) in acoustic obstacle scattering is considered. Under certain conditions it is proved that if the boundary partial derivati ve Gamma of an obstacle Gamma has finite upper delta -Minkowski content mu* (delta, delta Gamma), then there is a positive constant C-n,C-delta, depend ing only on n and delta, such that \s(lambda)-(2 pi)(-n)Wn \ Gamma \ (n)lambda (n)/(2)\ less than or equal to C-n,C-n-1 mu* (n - 1, delta Gamma) log lambda lambda (n-1)/(2), for delta = n-1, and \s(lambda)- (2 pi)(-n) W-n \ Gamma \ (n)lambda (n)/(2) less than or equal t o C-n,(delta mu)*(n -1, partial derivative Gamma)lambda (delta)/(2), for de lta is an element of (n -1, n), as lambda --> infinity, where w(n) is the v olume of the unit ball in R-n.