Gamma-liminf estimate for a class of non-local approximations of Sobolev and BV norms

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2025-06-18 DOI:10.1016/j.jfa.2025.111106

Massimo Gobbino, Nicola Picenni

引用次数: 0

Abstract

We consider a family of non-local and non-convex functionals, and we prove that their Gamma-liminf is bounded from below by a positive multiple of the Sobolev norm or the total variation. As a by-product, we answer some open questions concerning the limiting behavior of these functionals.

The proof relies on the analysis of a discretized version of these functionals.

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一类Sobolev范数和BV范数的非局部近似的极限估计

我们考虑了一类非局部非凸泛函，并证明了它们的极限由Sobolev范数或总变分的正倍数从下起有界。作为一个副产品，我们回答了一些关于这些泛函的极限行为的开放性问题。证明依赖于对这些泛函的离散化版本的分析。

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

Journal of Functional Analysis 数学-数学

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