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<p>In this paper, we prove a Talenti-type comparison theorem for the <i>p</i>-Laplacian with Dirichlet boundary conditions on open subsets of a <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\textrm{RCD}(0,N)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>RCD</mtext> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mi>N</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> space with <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(N\in (1,\infty )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mi>∞</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. We also obtain an almost rigidity result of the Talenti-type comparison theorem, whose proof relies on a compactness on varying spaces.</p>

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Almost Rigidity of the Talenti-Type Comparison Theorem on \(\textrm{RCD}(0,N)\) Spaces

  • 期刊论文

  • 发表日期：

    2026年3月19日

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  • Wenjing Wu

摘要

In this paper, we prove a Talenti-type comparison theorem for the p-Laplacian with Dirichlet boundary conditions on open subsets of a \(\textrm{RCD}(0,N)\) RCD ( 0 , N ) space with \(N\in (1,\infty )\) N ∈ ( 1 , ∞ ) . We also obtain an almost rigidity result of the Talenti-type comparison theorem, whose proof relies on a compactness on varying spaces.