Let M be a C²-smooth Riemannian manifold with boundary and X be a metric space with non-positive curvature in the sense of Alexandrov. Let u: M → X be a Sobolev mapping in the sense of Korevaar and Schoen. In this short note, we introduce a notion of p-energy for u which is slightly different from the original definition of Korevaar and Schoen. We show that each minimizing p-harmonic mapping (p ≥ 2) associated to our notion of p-energy is locally Holder continuous whenever its image lies in a compact subset of X.

中文翻译：

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NPC空间中P调和映射的正则性

令M为具有边界的C ²光滑黎曼流形，而X为在亚历山大的意义上具有非正曲率的度量空间。令u：M → X是在Korevaar和Schoen的意义上的Sobolev映射。在此简短的注释中，我们为u引入p能量的概念，该概念与Korevaar和Schoen的原始定义略有不同。我们表明，每减少p K谐波映射（p关联到我们的概念≥2）p -能量是本地持有人连续每当它的形象掌握在一个紧凑的子集X。