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<p>In this paper, we consider a broad class of nonlinear integro-differential problems in the Grushin-type space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathbb {G}}^{n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">G</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>, with the prototype being the Dirichlet problem for the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>fractional Laplace equation. We establish general Harnack inequalities and weak Harnack inequalities for the corresponding weak solutions to the integro-differential problems.</p>

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Nonlocal Harnack Inequalities in Grushin-type Spaces

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Boxiang Xu,
  • Yu Liu,
  • Shaoguang Shi

摘要

In this paper, we consider a broad class of nonlinear integro-differential problems in the Grushin-type space \({\mathbb {G}}^{n}\) G n , with the prototype being the Dirichlet problem for the \(p-\) p - fractional Laplace equation. We establish general Harnack inequalities and weak Harnack inequalities for the corresponding weak solutions to the integro-differential problems.