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<p>We investigate quasi-symmetry for small perturbations of the Gidas-Ni-Nirenberg problem involving the&#xa0;<i>p</i>-Laplacian and for small perturbations the critical&#xa0;<i>p</i>-Laplace equation for&#xa0;<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p&gt;2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>&gt;</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. To achieve these results, we provide a quantitative review of the work by Damascelli &amp; Sciunzi [<CitationRef CitationID="CR16">16</CitationRef>] concerning the weak Harnack comparison inequality and the local boundedness comparison inequality. Moreover, we prove a comparison principle for small domains.</p>

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Approximate radial symmetry for p-Laplace equations via the moving planes method

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月22日

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  • Michele Gatti

摘要

We investigate quasi-symmetry for small perturbations of the Gidas-Ni-Nirenberg problem involving the p-Laplacian and for small perturbations the critical p-Laplace equation for  \(p>2\) p > 2 . To achieve these results, we provide a quantitative review of the work by Damascelli & Sciunzi [16] concerning the weak Harnack comparison inequality and the local boundedness comparison inequality. Moreover, we prove a comparison principle for small domains.