带对流项的退化椭圆方程熵解的正则性

IF 0.7 4区数学 Q2 MATHEMATICS

Rocky Mountain Journal of Mathematics Pub Date : 2023-10-01 DOI:10.1216/rmj.2023.53.1469

Gao Hongya, Zhang Aiping, Huang Miaomiao

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引用次数: 0

摘要

我们处理退化椭圆方程的熵解为{- div(x,u(x))，∇u(x))= - div(u(x)|u(x)|θ - 1E(x))+f(x)，x∈Ω，u(x)=0,x∈∂Ω，其中，对于几乎所有的x∈Ω和所有的(s，ξ)∈∈∈，carathodory函数为(x,s，ξ)→ξ≥α| p(1+|s|)τ和可控制的生长条件| (x,s，ξ)|≤β|ξ|p−1。令1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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REGULARITY FOR ENTROPY SOLUTIONS TO DEGENERATE ELLIPTIC EQUATIONS WITH A CONVECTION TERM

We deal with entropy solutions to degenerate elliptic equations of the form { −div 𝒜(x,u(x),∇u(x))=−div(u(x)|u(x)|θ−1E(x))+f(x),x∈Ω,u(x)=0,x∈∂Ω, where the Carathéodory function 𝒜:Ω×ℝ×ℝn→ℝn satisfies degenerate coercivity condition 𝒜(x,s,ξ)⋅ξ≥α|ξ|p(1+|s|)τ and controllable growth condition |𝒜(x,s,ξ)|≤β|ξ|p−1 for almost all x∈Ω and all (s,ξ)∈ℝ×ℝn. We let 1

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来源期刊

Rocky Mountain Journal of Mathematics 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

7.5 months

期刊介绍： Rocky Mountain Journal of Mathematics publishes both research and expository articles in mathematics, and particularly invites well-written survey articles. The Rocky Mountain Journal of Mathematics endeavors to publish significant research papers and substantial expository/survey papers in a broad range of theoretical and applied areas of mathematics. For this reason the editorial board is broadly based and submissions are accepted in most areas of mathematics. In addition, the journal publishes specialized conference proceedings.