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<p>This paper is devoted to the study of the asymptotic behavior of the solution of the Dirichlet problem for the Laplace equation in the half-space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7637_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="223" /> </InlineMediaObject> <EquationSource Format="TEX">\({E}_{+}^{N+1}\equiv \left\{x,y:x\in {E}^{n},y&gt;0\right\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>E</mi> <mrow> <mo>+</mo> </mrow> <mrow> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>≡</mo> <mfenced close="}" open="{"> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>:</mo> <mi>x</mi> <mo>∈</mo> <msup> <mrow> <mi>E</mi> </mrow> <mi>n</mi> </msup> <mo>,</mo> <mi>y</mi> <mo>&gt;</mo> <mn>0</mn> </mfenced> </mrow> </math></EquationSource> </InlineEquation> for large values of the variable <i>y</i>.</p>

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Asymptotics of Solutions of the Dirichlet Problem for the Laplace Equation in the Half-Space

  • 期刊论文

  • 发表日期：

    2025年2月27日

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  • P. V. Denisov

摘要

This paper is devoted to the study of the asymptotic behavior of the solution of the Dirichlet problem for the Laplace equation in the half-space \({E}_{+}^{N+1}\equiv \left\{x,y:x\in {E}^{n},y>0\right\}\) E + N + 1 ≡ x , y : x ∈ E n , y > 0 for large values of the variable y.