1.Fakultat für Mathematik,Universitat Bielefeld,Bielefeld,Germany;2.Mathematical Institute,Charles University in Prague,Praha 8-Karlin,Czechia;3.Dipartimento di Matematica,Università di Napoli,Naples,Italy
Abstract:
We develop an improved version of the parabolic Lipschitz truncation, which allows qualitative control of the distributional time derivative and the preservation of zero boundary values. As a consequence, we establish a new caloric approximation lemma. We show that almost p-caloric functions are close to p-caloric functions. The distance is measured in terms of spatial gradients as well as almost uniformly in time. Both results are extended to the setting of Orlicz growth.