李东升,西安交通大学

In this talk, we will first go over the history of Schauder estimates, where the developing of proofs will be emphasized. Second, we will establish pointwise interior Schauder estimates for Stokes systems in divergence form with variable coefficients. The estimates are presented by Campanato's characterization and are attained by an iteration method which was originated by L.Caffarelli to study Schauder estimates for fully nonlinear elliptic equations. Although no continuity in time variable is assumed for the coefficients and the given data, Holder continuity of curls of velocities is surprisingly obtained in both spatial variables and time variable.