标题： 关于次临界广义$p$-调和映射进入齐次目标的 Sacks-Uhlenbeck 型正则性 显示英文标题

标题： Sacks-Uhlenbeck type regularity for subcritical generalized $p$-harmonic maps into Homogeneous targets

摘要： 借鉴\cite{strz3}的思想，我们定义了广义的$p$-调和映射到黎曼齐次目标空间的概念，这是一种不属于能量空间的解的定义。我们将注意力限制在次临界范围内，即当$p$大于定义域维度$n$时，我们在极限$p \searrow n$下，对于这一族映射序列证明了一个一致的$C^{1,\alpha}$-正则性结果，并假设其元素具有一个一致的$n$-能量上界。 证明的方法与\cite{strz3}中的方法完全相同，但我们需要检查之前未考虑的估计的一致性。 显示英文摘要

摘要： Adapting \cite{strz3}, we define generalized $p$-harmonic maps into Riemannian homogeneous targets, a notion of solutions not belonging to the energy space. Restricting our attention to the subcritical range $p$ greater than the domain dimension $n$, we show a uniform $C^{1,\alpha}$-regularity result for a sequence of such maps in the limit $p \searrow n$, assuming a uniform $n$-energy bound on its elements. The method of the proof follows the exact same lines as in \cite{strz3} but we need to check uniformity of estimates not previously considered there.