Sharp estimates of solution of an elliptic problem on a family of open non-convex planar sectors

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-08-30 DOI:10.1002/mma.10449

Abdelaziz Douah, Abdelkader Tami, Mounir Tlemcani

引用次数: 0

Abstract

Based on partial Fourier series analysis, we adapt on a model case a new approach to classical results obtained in the literature describing the singularities of a family a solutions of a second-order elliptic problems on open non-convex planar sectors. The method allows the exhibition of singular and regular frequencies, explicit decomposition, and description of coefficients of singularities of the solution. As a main result, explicit and sharp estimates with respect to the opening angle parameter are obtained via this method. They are not uniform near $π$ where corners have opening angle generating a jump of singularity in Sobolev exponent, contrarily to the results obtained for harmonic and/or biharmonic problems on a family of convex planar sectors.

查看原文本刊更多论文

开放非凸平面扇形族上椭圆问题解法的锐估计

基于偏傅里叶级数分析，我们在一个模型案例中采用了一种新方法，来处理文献中获得的描述开放非凸平面扇形上二阶椭圆问题解的奇异性的经典结果。这种方法可以显示奇异频率和规则频率、明确分解和描述解的奇异性系数。其主要结果是，通过该方法获得了关于开口角参数的明确而尖锐的估计值。与在凸平面扇形系列上的谐波和/或双谐波问题中获得的结果相反，在角的开口角产生索博廖夫指数奇异性跃迁的附近，这些估计值并不均匀。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.