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

Abstract

We prove a new $\mathcal{A}$-caloric approximation lemma compatible with an Orlicz setting. With this result, we establish a partial regularity result for parabolic systems of the type $$u_t-\mathrm{div}a(Du)=0.$$ Here the growth of $a$ is bounded by the derivative of an $N$-function $\phi$. The primary assumption for $\phi$ is that $t{\phi }^{\prime \prime }(t)$ and ${\phi }^{\prime }(t)$ are uniformly comparable on $(0,\infty )$.