Lipschitz 域中的准线性分阶算子

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-06-04 DOI:10.1137/23m1575871

Juan Pablo Borthagaray, Wenbo Li, Ricardo H. Nochetto

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引用次数: 0

摘要

SIAM 数学分析期刊》，第 56 卷第 3 期，第 4006-4039 页，2024 年 6 月。摘要。我们证明了[math]的 Lipschitz 域[math]上具有可变系数的分数阶准线性算子的同调 Dirichlet 问题解的 Besov 边界正则性。我们的估计与光滑域上解的边界行为一致，并适用于分数[math]-拉普拉奇和具有有限视界的算子。证明利用了底层变分结构，并使用了一个新的、灵活的局部平移算子。我们进一步应用这些正则性估计，推导出分数[math]-Laplacians 的有限元近似的新误差估计，并介绍了揭示解的边界行为的若干模拟。

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Quasi-linear Fractional-Order Operators in Lipschitz Domains

SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 4006-4039, June 2024.
Abstract. We prove Besov boundary regularity for solutions of the homogeneous Dirichlet problem for fractional-order quasi-linear operators with variable coefficients on Lipschitz domains [math] of [math]. Our estimates are consistent with the boundary behavior of solutions on smooth domains and apply to fractional [math]-Laplacians and operators with finite horizon. The proof exploits the underlying variational structure and uses a new and flexible local translation operator. We further apply these regularity estimates to derive novel error estimates for finite element approximations of fractional [math]-Laplacians and present several simulations that reveal the boundary behavior of solutions.

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.