Higher Hölder regularity for the fractional p-Laplace equation in the subquadratic case

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-05-24 DOI:10.1007/s00208-024-02891-z

Prashanta Garain, Erik Lindgren

引用次数: 0

Abstract

We study the fractional p-Laplace equation

$$\begin{aligned} (-\Delta _p)^s u = 0 \end{aligned}$$

for $0<s<1$ and in the subquadratic case $1<p<2$. We provide Hölder estimates with an explicit Hölder exponent. The inhomogeneous equation is also treated and there the exponent obtained is almost sharp for a certain range of parameters. Our results complement the previous results for the superquadratic case when $p\ge 2$. The arguments are based on a careful Moser-type iteration and a perturbation argument.

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分式 p 拉普拉斯方程在亚二次方程情况下的较高荷尔德正则性

我们研究了分数 p-Laplace 方程 $$begin{aligned} (-\Delta _p)^s u = 0 \end{aligned}$$对于（0<s<1\）和亚二次方程情况下（1<p<2\）。我们提供了具有明确霍尔德指数的霍尔德估计值。我们还处理了非均质方程，在那里，对于一定范围的参数，所得到的指数几乎是尖锐的。我们的结果补充了之前针对超二次方程的结果，即当 $p\ge 2$ 时。这些论证基于谨慎的 Moser 型迭代和扰动论证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.