BIFURCATION STRUCTURE TO SERRIN’S OVERDETERMINED PROBLEM

IF 0.7 4区数学 Q2 MATHEMATICS

Rocky Mountain Journal of Mathematics Pub Date : 2023-10-01 DOI:10.1216/rmj.2023.53.1445

Guowei Dai, Fang Liu, Qingbo Liu

引用次数: 0

Abstract

We study the bifurcation structure to Serrin’s overdetermined problem such that −Δu=1 in Ω, u=0, ∂νu= const on ∂Ω. We prove that the bifurcation from the straight cylinder Bλ1×ℝ with λ1>0 is critical at the bifurcation point. Moreover, we obtain the global structure of bifurcation branches. To study the global structure of bifurcation branches, we establish a global bifurcation theorem in finite dimensional space.

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serrin超定问题的分岔结构

我们研究了Serrin的过定问题的分支结构，使得在Ω中−Δu=1，在∂Ω中u=0，∂νu= const。证明了λ1>0的直线圆柱体b λ 1x的分岔在分岔点处是临界的。此外，我们还得到了分支的全局结构。为了研究分岔分支的整体结构，在有限维空间中建立了一个整体分岔定理。

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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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.