加权索波列夫空间中具有一般稳定算子的非局部椭圆和抛物方程

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-02 DOI:10.1137/23m160061x

Hongjie Dong, Junhee Ryu

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引用次数: 0

摘要

SIAM 数学分析期刊》，第 56 卷，第 4 期，第 4623-4661 页，2024 年 8 月。摘要。我们研究加权索波列夫空间[math]开集上的非局部椭圆方程和抛物方程，其中[math].我们考虑的算子是对称稳定莱维过程的无穷小发生器，允许其莱维量非常奇异。此外，对于抛物线方程，我们假定其度量仅在时间变量中可测量。

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Nonlocal Elliptic and Parabolic Equations with General Stable Operators in Weighted Sobolev Spaces

SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4623-4661, August 2024.
Abstract. We study nonlocal elliptic and parabolic equations on [math] open sets in weighted Sobolev spaces, where [math]. The operators we consider are infinitesimal generators of symmetric stable Lévy processes, whose Lévy measures are allowed to be very singular. Additionally, for parabolic equations, the measures are assumed to be merely measurable in the time variable.

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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.