关于多边形域拉普拉斯变换定理的注解

IF 0.7 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics Pub Date : 2024-12-11 DOI:10.21136/AM.2024.0049-24

Jens Markus Melenk, Claudio Rojik

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引用次数: 0

摘要

对于Dirichlet， Neumann和混合边界条件，我们给出了有限平面锥（因此也在平面多边形上）泊松方程解的移位定理。平移定理的适用范围取决于圆锥的角度。对于值域的右端点，移位定理用Besov空间而不是Sobolev空间来描述。

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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A note on the shift theorem for the Laplacian in polygonal domains

We present a shift theorem for solutions of the Poisson equation in a finite planar cone (and hence also on plane polygons) for Dirichlet, Neumann, and mixed boundary conditions. The range in which the shift theorem holds depends on the angle of the cone. For the right endpoint of the range, the shift theorem is described in terms of Besov spaces rather than Sobolev spaces.

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来源期刊

Applications of Mathematics 数学-应用数学

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Applications of Mathematics publishes original high quality research papers that are directed towards applications of mathematical methods in various branches of science and engineering. The main topics covered include: - Mechanics of Solids; - Fluid Mechanics; - Electrical Engineering; - Solutions of Differential and Integral Equations; - Mathematical Physics; - Optimization; - Probability Mathematical Statistics. The journal is of interest to a wide audience of mathematicians, scientists and engineers concerned with the development of scientific computing, mathematical statistics and applicable mathematics in general.