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<p>In this paper, we prove the fractional discrete Sobolev inequality and concentration-compactness principle at infinity for the fractional Laplacian on lattice graphs <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {Z}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation>. As an application, we show the existence of extremal function for a supercritical fractional discrete Sobolev inequality.</p>

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The Concentration-Compactness Principle for the Fractional Laplacian on Lattice Graphs

  • 期刊论文

  • 发表日期：

    2026年6月22日

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  • Lidan Wang,
  • Yanhua Zhao

摘要

In this paper, we prove the fractional discrete Sobolev inequality and concentration-compactness principle at infinity for the fractional Laplacian on lattice graphs \(\mathbb {Z}^d\) Z d . As an application, we show the existence of extremal function for a supercritical fractional discrete Sobolev inequality.