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Regularity of quasi-n-harmonic mappings into NPC spaces

Chang-Yu Guo, Chang-Lin Xiang

Abstract

We prove local Holder continuity of quasi-n-harmonic mappings from Euclidean domains into metric spaces with non-positive curvature in the sense of Alexandrov. We also obtain global Holder continuity of such mappings from bounded Lipschitz domains.

Regularity of quasi-n-harmonic mappings into NPC spaces

Abstract

We prove local Holder continuity of quasi-n-harmonic mappings from Euclidean domains into metric spaces with non-positive curvature in the sense of Alexandrov. We also obtain global Holder continuity of such mappings from bounded Lipschitz domains.

Paper Structure

This paper contains 9 sections, 4 theorems, 49 equations.

Table of Contents

  1. Introduction and main results
  2. Background
  3. Main results
  4. Outline of proof
  5. Preliminaries
  6. Sobolev mappings with value in metric spaces
  7. Metric spaces with non-positive curvature in the sense of Alexandrov
  8. Pullback tensors
  9. Proof of main results

Key Result

Theorem 1.2

Let $\Omega\subset {\mathbb R}^n$ be a domain and $X$ an NPC space. Then each $Q$-quasi-$n$-harmonic mapping $u\colon \Omega\to X$ has a locally $\alpha$-Hölder continuous representative for some $\alpha$ depending only on $Q$ and $n$.

Theorems & Definitions (10)

  • Definition 1.1
  • Theorem 1.2
  • Corollary 1.3
  • Theorem 1.4
  • Lemma 2.1
  • proof
  • Remark 2.2
  • Definition 2.3: NPC spaces
  • proof : Proof of Theorem \ref{['thm:main theorem']}
  • proof : Proof of Theorem \ref{['thm:boundary regularity']}