论文标题
$ \ MATHCAL {A} $ - 抛物线系统的热量近似和部分规律性具有Orlicz增长
$\mathcal{A}$-caloric approximation and partial regularity for parabolic systems with Orlicz growth
论文作者
论文摘要
我们证明了一种新的$ \ Mathcal {a} $ - 卡路里近似引理与Orlicz设置兼容。通过此结果，我们为类型$$ u_ {t} - {\ rm div} \，a（du）= 0的抛物线系统建立了部分规则性结果。 $$这里的$ a $的增长受$ n $ function $φ$的派生范围。 $φ$的主要假设是$tφ''（t）$和$φ'（t）$在$（0，\ infty）$上均均匀地比较。
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 $$ u_{t}- {\rm div} \,a(Du)=0. $$ Here the growth of $a$ is bounded by the derivative of an $N$-function $φ$. The primary assumption for $φ$ is that $tφ''(t)$ and $φ'(t)$ are uniformly comparable on $(0,\infty)$.
