Interior pointwise $C^{1,α}$ estimates for Stokes systems in divergence form

Rong Dong; Dongsheng Li

paper

Interior pointwise $C^{1, α}$ estimates for Stokes systems in divergence form

arXiv:2304.03529

Abstract

Interior pointwise $C^{1, α}$ estimates are established for Stokes systems in divergence form where no continuity in time variable is assumed for the coefficients and the given data. The estimates are attained by iteration and are presented by Campanato's characterization. The sharpness of the conclusions can be seen from Serrin's counterexample.

21 pages

Interior pointwise C1,α estimates for Stokes systems in divergence form

Abstract

Interior pointwise $C^{1, α}$ estimates for Stokes systems in divergence form