Regularity of weak solutions to linear and quasilinear parabolic systems of non-divergence type with non-smooth in time principal matrix: A(t)-caloric method

Abstract

We prove a modification of the so-called A(t)-caloric lemma stated in our earlier work with O. John [1] to study regularity of weak solutions to parabolic systems of non-divergence type with non-smooth in time principal matrices.

As an application, we prove smoothness results in Morrey and Campanato spaces for linear parabolic systems of non-divergence type by the A(t)-caloric approximation method.

Keywords

• Non-divergence parabolic systems
• non-smooth in time coefficients
• regularity of weak solutions
• Lambda(t)-caloric approximation