Wontae Kim

Parabolic Poincar\'e inequalities and maximal function estimates for systems of partial differential equations

We study parabolic Poincar\'e inequalities for solutions to nonlinear systems of partial differential equations. Our main results show that these inequalities are self-improving. As applications, we establish reverse H\"older inequalities for the mean oscillation over parabolic cylinders and for the gradient. We also c...