Steklov vs. Steklov：与Babuška悖论相关的四阶事件

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2025-07-24 DOI:10.1016/j.nonrwa.2025.104464

Francesco Ferraresso , Pier Domenico Lamberti

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引用次数: 0

摘要

我们讨论了两个四阶Steklov问题，并强调了通过凸多边形序列在凸域上的逼近中出现的Babuška悖论。为此，我们证明了这两个问题之一的特征值依赖于凸域类的域摄动的连续性，扩展了文献中已知的第一个特征值的结果。这是通过详细研究由Ferrero， Gazzola和Weth引入的调和函数的非局部二阶问题而得到的。我们进一步回顾了该结果如何与铰链板的经典Babuška悖论的各种变体以及Maz 'ya和Nazarov的退化结果相关联。

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Steklov vs. Steklov: A fourth-order affair related to the Babuška paradox

We discuss two fourth-order Steklov problems and highlight a Babuška paradox appearing in their approximations on convex domains via sequences of convex polygons. To do so, we prove that the eigenvalues of one of the two problems depend with continuity upon domain perturbation in the class of convex domains, extending a result known in the literature for the first eigenvalue. This is obtained by examining in detail a nonlocal second order problem for harmonic functions introduced by Ferrero, Gazzola, and Weth. We further review how this result is connected to diverse variants of the classical Babuška paradox for the hinged plate and to a degeneration result by Maz’ya and Nazarov.

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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.