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We prove a modification of the so-calledA  ⁢   (  t  )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 theA  ⁢   (  t  )A(t)   -caloric approximation method.

forum mathematicum

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