Title: Vectorial Kato inequality for $p$-harmonic maps with optimal constant Show Chinese title

Title: 向量型Kato不等式对于具有最佳常数的$p$-调和映射的应用

Abstract: We derive the sharp vectorial Kato inequality for $p$-harmonic mappings. Surprisingly, the optimal constant differs from the one obtained for scalar valued $p$-harmonic functions by Chang, Chen, and Wei. As an application we demonstrate how this inequality can be used in the study of regularity of $p$-harmonic maps. Furthermore, in the case of $p$-harmonic maps from $B^3$ to $\mathbb{S}^3$, we enhance the known range of $p$ values for which regularity is achieved. Specifically, we establish that for $p \in [2, 2.642]$, minimizing $p$-harmonic maps must be regular. Show Chinese abstract

Abstract: 我们推导出了关于$p$-调和映射的尖锐矢量型Kato不等式。令人惊讶的是，最优常数与Chang、Chen和Wei对于标量值$p$-调和函数所获得的常数不同。作为应用，我们展示了该不等式如何用于研究$p$-调和映射的正则性。此外，在从$B^3$到$\mathbb{S}^3$的$p$-调和映射的情形下，我们改进了已知的能够保证正则性的$p$值的范围。 具体来说，我们证明了对于$p \in [2, 2.642]$，最小化$p$-调和映射必须是正则的。