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<p>In this paper, we consider degenerate quasilinear elliptic models of normalized <i>p</i>-Laplacian type. We establish local <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11118_2025_10228_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^{1,\alpha '}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mrow> <mn>1</mn> <mo>,</mo> <msup> <mi>α</mi> <mo>′</mo> </msup> </mrow> </msup> </math></EquationSource> </InlineEquation> regularity of viscosity solutions by making use of the compactness argument, scaling techniques and the localized oscillating method. In addition, we also obtain almost optimal pointwise <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11118_2025_10228_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^{1,\tau } \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>τ</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> regularity for degenerate free transmission problem related to normalized <i>p</i>-Laplacian. Our argument is based on a new improved oscillation-type estimate combined with a localized analysis.</p>

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Regularity of Solutions to Degenerate Normalized p-Laplacian Equation with General Variable Exponents

  • 期刊论文

  • 发表日期：

    2025年5月27日

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  • Jiangwen Wang,
  • Yunwen Yin,
  • Feida Jiang

摘要

In this paper, we consider degenerate quasilinear elliptic models of normalized p-Laplacian type. We establish local \(C^{1,\alpha '}\) C 1 , α ′ regularity of viscosity solutions by making use of the compactness argument, scaling techniques and the localized oscillating method. In addition, we also obtain almost optimal pointwise \(C^{1,\tau } \) C 1 , τ regularity for degenerate free transmission problem related to normalized p-Laplacian. Our argument is based on a new improved oscillation-type estimate combined with a localized analysis.