外部域上 (p(y),q(y))-拉普拉斯椭圆问题解的存在性

Pub Date : 2024-04-25 DOI:10.1515/gmj-2024-2022

Akanksha Kesarwani, Rasmita Kar

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stretchy=\"false\">)</m:mo>\n </m:mrow>\n <m:mo>⁢</m:mo>\n <m:msup>\n <m:mrow>\n <m:mo stretchy=\"false\">|</m:mo>\n <m:mi>v</m:mi>\n <m:mo stretchy=\"false\">|</m:mo>\n </m:mrow>\n <m:mrow>\n <m:mrow>\n <m:mi>p</m:mi>\n <m:mo>⁢</m:mo>\n <m:mrow>\n <m:mo stretchy=\"false\">(</m:mo>\n <m:mi>y</m:mi>\n <m:mo stretchy=\"false\">)</m:mo>\n </m:mrow>\n </m:mrow>\n <m:mo>-</m:mo>\n <m:mn>2</m:mn>\n </m:mrow>\n </m:msup>\n <m:mo>⁢</m:mo>\n <m:mi>v</m:mi>\n </m:mrow>\n </m:mrow>\n <m:mo>-</m:mo>\n <m:mrow>\n <m:mi>div</m:mi>\n <m:mo>⁡</m:mo>\n <m:mrow>\n <m:mo stretchy=\"false\">(</m:mo>\n <m:mrow>\n <m:msup>\n <m:mrow>\n <m:mo stretchy=\"false\">|</m:mo>\n <m:mrow>\n <m:mo>∇</m:mo>\n <m:mo>⁡</m:mo>\n <m:mi>v</m:mi>\n </m:mrow>\n <m:mo stretchy=\"false\">|</m:mo>\n </m:mrow>\n <m:mrow>\n <m:mrow>\n <m:mi>q</m:mi>\n <m:mo>⁢</m:mo>\n <m:mrow>\n <m:mo stretchy=\"false\">(</m:mo>\n <m:mi>y</m:mi>\n 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引用次数: 0

摘要

本文研究了以下涉及 ( p ( y ) , q ( y ) {p(y),q(y)} )- 拉普拉卡算子的椭圆问题： { - div ( a ( y ) | ∇ v | p ( y ) - 2 ∇ v ) + b ( y ) | v

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Existence of solutions for (p(y),q(y))-Laplacian elliptic problem on an exterior domain

In this paper, we study the following elliptic problem involving the ( p ⁢ ( y ) , q ⁢ ( y )

{p(y),q(y)}

)-Laplacian operator:

{ - div ⁡ ( a ⁢ ( y ) ⁢ | ∇ ⁡ v | p ⁢ ( y ) - 2 ⁢ ∇ ⁡ v ) + b ⁢ ( y ) ⁢ | v | p ⁢ ( y ) - 2 ⁢ v - div ⁡ ( | ∇ ⁡ v | q ⁢ ( y

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