Sobolev满足Besov：具有Dirichlet、Neumann和混合边值的Poisson方程的正则性

IF 2 2区数学 Q1 MATHEMATICS

Analysis and Applications Pub Date : 2021-02-19 DOI:10.1142/s0219530522500026

C. Schneider, Flóra Orsolya Szemenyei

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引用次数: 1

摘要

我们研究了具有Dirichlet、Neumann和混合边值的Poisson方程在多面体锥[公式：见正文]中的解在Besov空间的特定尺度[公式：参见正文]下的正则性。这些空间中解的正则性决定了自适应和非线性数值格式可以实现的近似阶数。我们的目的是对所研究的所有设置中的齐次和非齐次边界数据进行彻底的讨论，并表明在所有情况下，与分数Sobolev尺度[公式：见正文]相比，在特定的Besov尺度下的解要平滑得多，这证明了自适应方案的使用是合理的。

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Sobolev meets Besov: Regularity for the Poisson equation with Dirichlet, Neumann and mixed boundary values

We study the regularity of solutions of the Poisson equation with Dirichlet, Neumann and mixed boundary values in polyhedral cones [Formula: see text] in the specific scale [Formula: see text] of Besov spaces. The regularity of the solution in these spaces determines the order of approximation that can be achieved by adaptive and nonlinear numerical schemes. We aim for a thorough discussion of homogeneous and inhomogeneous boundary data in all settings studied and show that the solutions are much smoother in this specific Besov scale compared to the fractional Sobolev scale [Formula: see text] in all cases, which justifies the use of adaptive schemes.

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来源期刊

Analysis and Applications 数学-数学

CiteScore

3.90

自引率

4.50%

发文量

审稿时长

>12 weeks

期刊介绍： Analysis and Applications publishes high quality mathematical papers that treat those parts of analysis which have direct or potential applications to the physical and biological sciences and engineering. Some of the topics from analysis include approximation theory, asymptotic analysis, calculus of variations, integral equations, integral transforms, ordinary and partial differential equations, delay differential equations, and perturbation methods. The primary aim of the journal is to encourage the development of new techniques and results in applied analysis.