BOUNDS FOR THE GRADIENT OF THE TRANSITION KERNEL FOR ELLIPTIC OPERATORS WITH UNBOUNDED DIFFUSION, DRIFT AND POTENTIAL TERMS

被引：0

作者：

Kunze, Markus ^{[1
]}

Porfido, Marianna ^{[2
]}

Rhandi, Abdelaziz ^{[2
]}

机构：

[1] Univ Konstanz, Fachbereich Math & Stat, D-78457 Constance, Germany

[2] Univ Salerno, Dipartimento Matemat, Via Giovanni Paolo II 132, I-84084 Fisciano, SA, Italy

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2024年 / 17卷 / 5-6期

关键词：

Parabolic equation with unbounded coefficients; heat kernel estimates; estimates of the derivative; one-parameter semigroup;

D O I：

10.3934/dcdss.2023091

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Global Sobolev regularity and pointwise upper bounds for the gradient of transition densities associated with second order elliptic operators in R-d was obtained in the case of bounded diffusion coefficients in [13, Section 5]. In this paper we generalize these results to the case of unbounded diffusions. Our technique is based on an approximation procedure and a De Giorgi type regularity result. We like to point out, that such an approximation procedure cannot be applied to the result in [13], since the constants in the estimates obtained in [13] depend on the infinity norm of the diffusion coefficients.

引用

页码：2141 / 2172

页数：32

共 47 条

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[47] Elliptic operators with unbounded diffusion and singular lower order terms in Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-spaces
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