A REGULARITY THEORY FOR PARABOLIC EQUATIONS WITH ANISOTROPIC NONLOCAL OPERATORS IN SPACES

被引：1

作者：

Choi, Jae-hwan ^{[1
]}

Kang, Jaehoon ^{[2
]}

Parks, Daehan ^{[3
]}

机构：

[1] Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon 34141, South Korea

[2] Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea

[3] Korea Inst Adv Study, Sch Math, Seoul 02455, South Korea

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2024年 / 56卷 / 01期

关键词：

anisotropic nonlocal operator; Sobolev regularity; Levy process; INTEGRODIFFERENTIAL EQUATIONS; HARNACK PRINCIPLE; CAUCHY-PROBLEM;

D O I：

10.1137/23M1574944

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present an Lq(Lp)-regularity theory for parabolic equations of the operators encompassing the singular anisotropic fractional Laplacian with measurable coefficients: i=1 | yi| 1+\alpha i dyi. To address the anisotropy of the operator, we employ a probabilistic representation of the solution and Calder\'on-Zygmund theory. As applications of our results, we demonstrate the solvability of elliptic equations with anisotropic nonlocal operators and parabolic equations with isotropic nonlocal operators.

引用

页码：1264 / 1299

页数：36

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