On $$L_{p}-$$ Theory for Integro-Differential Operators with Spatially Dependent Coefficients

IF 1 3区数学 Q1 MATHEMATICS Potential Analysis Pub Date : 2024-03-14 DOI:10.1007/s11118-024-10131-x

Sutawas Janreung, Tatpon Siripraparat, Chukiat Saksurakan

引用次数: 0

Abstract

The parabolic integro-differential Cauchy problem with spatially dependent coefficients is considered in generalized Bessel potential spaces where smoothness is defined by Lévy measures with O-regularly varying profile. The coefficients are assumed to be bounded and Hölder continuous in the spatial variable. Our results can cover interesting classes of Lévy measures that go beyond those comparable to $dy/\left| y\right| ^{d+\alpha }.$

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关于具有空间依赖系数的积分微分算子的 $$L_{p}-$$ 理论

在广义贝塞尔势空间中考虑了具有空间依赖系数的抛物线积分微分考奇问题，其平稳性由具有 O 型规则变化轮廓的莱维量定义。假设系数在空间变量中是有界和赫尔德连续的。我们的结果可以涵盖有趣的 Lévy 测量类别，这些类别超出了与$dy/\left|y/\right| ^{d+\alpha }.$类似的测量。

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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来源期刊

Potential Analysis 数学-数学

CiteScore

2.20

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; boundary value problems, Martin boundaries, Poisson boundaries, etc.