Harnack inequality for parabolic equations with coefficients depending on time

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-04-20 DOI:10.1515/acv-2021-0055

F. Paronetto

引用次数: 1

Abstract

Abstract We define a homogeneous De Giorgi class of order p = 2 {p=2} that contains the solutions of evolution equations of the types ξ ⁢ ( x , t ) ⁢ u t + A ⁢ u = 0 {\xi(x,t)u_{t}+Au=0} and ( ξ ⁢ ( x , t ) ⁢ u ) t + A ⁢ u = 0 {(\xi(x,t)u)_{t}+Au=0} , where ξ > 0 {\xi>0} almost everywhere and A is a suitable elliptic operator. For functions belonging to this class, we prove a Harnack inequality. As a byproduct, one can obtain Hölder continuity for solutions of a subclass of the first equation.

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系数随时间变化的抛物型方程的Harnack不等式

摘要我们定义了一个p＝2｛p＝2｝阶齐次De Giorgi类，它包含类型为ξ（x，t）u t+a u＝0｛\neneneba xi（x，t）u _｛t｝+Au＝0｝和（ξ（x，t）u）t+a u＝0｛。对于属于这一类的函数，我们证明了一个Harnack不等式。作为副产品，可以获得第一个方程的子类解的Hölder连续性。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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