拟绝对最小 Lipschitz 延拓存在性的一般定理
泛函分析
2014-07-22 v3 偏微分方程分析
经典分析与常微分方程
摘要
本文考虑了一类广义 Lipschitz 延拓问题及其对应的寻找绝对最小 Lipschitz 延拓的问题。我们证明，如果存在最小 Lipschitz 延拓，那么在其它某些温和条件下，拟绝对最小 Lipschitz 延拓也必然存在。此处使用限定词“拟”是指所讨论的延拓函数在若干可任意小的因子范围内，几乎满足成为绝对最小 Lipschitz 延拓的条件。
引用
@article{arxiv.1211.5700,
title = {A general theorem of existence of quasi absolutely minimal Lipschitz extensions},
author = {Matthew J. Hirn and Erwan Le Gruyer},
journal= {arXiv preprint arXiv:1211.5700},
year = {2014}
}
备注
33 pages. v3: Correction to Example 2.4.3. Specifically, alpha-H\"older continuous functions, for alpha strictly less than one, do not satisfy (P3). Thus one cannot conclude that quasi-AMLEs exist in this case. Please note that the error remains in the published version of the paper in Mathematische Annalen. v2: Several minor corrections and edits, a new appendix (Appendix A)