An asymptotic sharp Sobolev regularity for planar infinity harmonic functions

被引：13

作者：

Koch, Herbert ^{[1
]}

Zhang, Yi Ru-Ya ^{[2
]}

Zhou, Yuan ^{[3
]}

机构：

[1] Univ Bonn, Inst Math, Endenicher Allee 60, D-53115 Bonn, Germany

[2] Hausdorff Ctr Math, Endenicher Allee 62, D-53115 Bonn, Germany

[3] Beihang Univ, Dept Math, Beijing 100191, Peoples R China

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2019年 / 132卷

关键词：

infinity-harmonic function; Absolute minimizer; Sobolev regularity; MINIMIZATION PROBLEMS; LIPSCHITZ EXTENSIONS; LAPLACIAN;

D O I：

10.1016/j.matpur.2019.02.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given an arbitrary planar infinity-harmonic function u, for each alpha > 0 we establish a quantitative W-loc(1,2)-estimate of vertical bar Du vertical bar(alpha), which is sharp as alpha -> 0. We also show that the distributional determinant of u is a Radon measure enjoying some quantitative lower and upper bounds. As a by-product, for each p > 2 we obtain some quantitative W-loc(1,p)-estimates of u, and consequently, an L-p-Liouville property for infinity-harmonic functions in the whole plane. (C) 2019 Elsevier Masson SAS. All rights reserved.

引用

页码：457 / 482

页数：26

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