Scholarlink

<p>We estimate the Hausdorff dimension of a subset of the boundary where a positive solution of the hyperbolic Lane–Emden equation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(-\Delta _{{\mathbb {B}}}u=u^p\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <msub> <mi mathvariant="normal">Δ</mi> <mi mathvariant="double-struck">B</mi> </msub> <mi>u</mi> <mo>=</mo> <msup> <mi>u</mi> <mi>p</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(0&lt;p&lt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>&lt;</mo> <mi>p</mi> <mo>&lt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> in the unit ball of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\mathbb {R}}^N\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> </math></EquationSource> </InlineEquation> grows faster than a prescribed order.</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

Boundary Growth Rates of Positive Solutions of Sublinear Elliptic Equations in the Real Hyperbolic Ball

  • 期刊论文

  • 发表日期：

    2025年2月10日

查看全文
  • Kentaro Hirata

摘要

We estimate the Hausdorff dimension of a subset of the boundary where a positive solution of the hyperbolic Lane–Emden equation \(-\Delta _{{\mathbb {B}}}u=u^p\) - Δ B u = u p with \(0<p<1\) 0 < p < 1 in the unit ball of \({\mathbb {R}}^N\) R N grows faster than a prescribed order.