On the Continuity of Bounded Weak Solutions to Parabolic Equations and Systems with Quadratic Growth in Gradients

Abstract

We establish the pointwise continuity of bounded weak solutions to of a class of scalar parabolic equations and strongly coupled parabolic systems. Our approach to the regularity theory of parabolic scalar equations is quite elementary and its applications to strongly coupled systems does not require higher $L^p$ integrability of derivatives.

arXiv admin note: text overlap with arXiv:2105.08615