Scholarlink

<p>We consider the equation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(- \Delta _{p} u = f(x)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <msub> <mi mathvariant="normal">Δ</mi> <mi>p</mi> </msub> <mi>u</mi> <mo>=</mo> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Omega ,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ω</mi> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> where <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\Delta _{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Δ</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> is the <i>p</i>-Laplace operator. We provide <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(L^{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>∞</mi> </msup> </math></EquationSource> </InlineEquation>-type estimates for the second derivatives of solutions when <i>p</i> approaches to 2.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Local behaviour of the second order derivatives of solutions to p-Laplace equations

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年10月18日

查看全文
  • Felice Iandoli,
  • Domenico Vuono

摘要

We consider the equation \(- \Delta _{p} u = f(x)\) - Δ p u = f ( x ) in \(\Omega ,\) Ω , where \(\Delta _{p}\) Δ p is the p-Laplace operator. We provide \(L^{\infty }\) L ∞ -type estimates for the second derivatives of solutions when p approaches to 2.