Special Session 10: Recent Developments in Regularity Theory for PDEs

Stationary Stokes systems in non-divergence and double divergence form
Jongkeun Choi
Pusan National University
Korea
Co-Author(s):    Seick Kim
Abstract:
We study stationary Stokes systems in non-divergence form with DMO coefficients and data. We prove that if $(u, p)$ is a strong solution of the system, then $(D^2u, \nabla p)$ is continuous. The corresponding boundary regularity result on a $C^{2, \rm Dini}$ domain is also established. To this end, we introduce the adjoint system associated with the non-divergence form Stokes system, which is formulated in double divergence form.