$$\mathcal {A}$$-caloric approximation and partial regularity for parabolic systems with Orlicz growth

Abstract

AbstractWe prove a new $$\mathcal {A}$$ A -caloric approximation lemma compatible with an Orlicz setting. With this result, we establish a partial regularity result for parabolic systems of the type $$\begin{aligned} u_{t}- {{\,\textrm{div}\,}}a(Du)=0. \end{aligned}$$ u t - div a ( D u ) = 0 . Here the growth of a is bounded by the derivative of an N-function $${\varphi }$$ φ . The primary assumption for $${\varphi }$$ φ is that $$t{\varphi }''(t)$$ t φ ′ ′ ( t ) and $${\varphi }'(t)$$ φ ′ ( t ) are uniformly comparable on $$(0,\infty )$$ ( 0 , ∞ ) .