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
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.
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页码:2141 / 2172
页数:32
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