On a Hardy–Morrey inequality

IF 1.7 2区 数学 Q1 MATHEMATICS
Ryan Hynd , Simon Larson , Erik Lindgren
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引用次数: 0

Abstract

Morrey's classical inequality implies the Hölder continuity of a function whose gradient is sufficiently integrable. Another consequence is the Hardy-type inequalityλudΩ1n/ppΩ|Du|pdx for any open set ΩRn. This inequality is valid for functions supported in Ω and with λ a positive constant independent of u. The crucial hypothesis is that the exponent p exceeds the dimension n. This paper aims to develop a basic theory for this inequality and the associated variational problem. In particular, we study the relationship between the geometry of Ω, sharp constants, and the existence of a nontrivial u which saturates the inequality.
关于Hardy-Morrey不等式
Morrey的经典不等式暗示了一个函数的Hölder连续性,其梯度是充分可积的。另一个结果是hardy型不等式λ udΩ1−n/p‖∞p≤∫Ω|Du|pdx对于任何开集Ω≠Rn。这个不等式对Ω中支持的函数有效,并且λ是独立于u的正常数。关键的假设是指数p超过维数n。本文旨在为这个不等式和相关的变分问题建立一个基本理论。特别地,我们研究了Ω的几何性质、尖锐常数和饱和不等式的非平凡u的存在性之间的关系。
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来源期刊
CiteScore
3.20
自引率
5.90%
发文量
271
审稿时长
7.5 months
期刊介绍: The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis
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