  Sharp Strichartz estimates are proved for Schr\"odinger and wave equations
with Lipschitz coefficients satisfying additional structural assumptions. We
use Phillips functional calculus as a substitute for Fourier inversion, which
shows how dispersive properties are inherited from the constant coefficient
case. Global Strichartz estimates follow provided that the derivatives of the
coefficients are integrable. The estimates extend to structured coefficients of
bounded variations. As applications we derive Strichartz estimates with
additional derivative loss for wave equations with H\"older-continuous
coefficients and solve nonlinear Schr\"odinger equations. Finally, we record
spectral multiplier estimates, which follow from the Strichartz estimates by
well-known means.
