Scholarlink

<p>In this paper we investigate the asymptotic behavior of anisotropic fractional energies as the fractional parameter <i>s</i> ∈ (0, 1) approaches both <i>s</i> ↑ 1 and <i>s</i> ↓ 0 in the spirit of the celebrated papers of Bourgain–Brezis–Mironescu [<CitationRef CitationID="CR5">5</CitationRef>] and Maz’ya–Shaposhnikova [<CitationRef CitationID="CR19">19</CitationRef>].</p><p>Then, focusing on the case <i>s</i> ↑ 1 we analyze the behavior of solutions to the corresponding minimization problems and finally, we also study the problem where a homogenization effect is combined with the localization phenomenon that occur when <i>s</i> ↑ 1.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Asymptotic behavior for anisotropic fractional energies

  • 期刊论文

  • 发表日期：

    2025年12月11日

查看全文
  • Julian Fernández Bonder,
  • Ariel Salort

摘要

In this paper we investigate the asymptotic behavior of anisotropic fractional energies as the fractional parameter s ∈ (0, 1) approaches both s ↑ 1 and s ↓ 0 in the spirit of the celebrated papers of Bourgain–Brezis–Mironescu [5] and Maz’ya–Shaposhnikova [19].

Then, focusing on the case s ↑ 1 we analyze the behavior of solutions to the corresponding minimization problems and finally, we also study the problem where a homogenization effect is combined with the localization phenomenon that occur when s ↑ 1.