用合适的低阶项逼近抛物周期均匀化中的两球一柱不等式

IF 0.9 3区数学 Q1 MATHEMATICS

Annali di Matematica Pura ed Applicata Pub Date : 2025-01-28 DOI:10.1007/s10231-025-01544-5

Yiping Zhang

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引用次数: 0

摘要

本文继续研究抛物周期均匀化中小的近似传播[j]。分析的。其中，利用基本解的渐近性质和拉格朗日插值技术，得到了抛物均匀化中近似的两球一圆柱不等式。本文研究了具有合适的低阶项的抛物型方程的齐次化问题，证明了近似的两球一柱不等式继续成立。难点在于如何处理抛物线均匀化中较“差”的次系数。本文所得到的结果可以很容易地推广到椭圆情况，这也是椭圆均匀化中的一个新问题。

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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Approximate two-sphere one-cylinder inequality in parabolic periodic homogenization with suitable lower-order terms

We continue the study of approximate propagation of smallness in parabolic periodic homogenization in [SIAM J. Math. Anal., 53(5):5835–5852, 2021], where by using the asymptotic behaviors of fundamental solutions and the Lagrange interpolation technique, we obtained the approximate two-sphere one-cylinder inequality in parabolic homogenization. In this paper, we consider the parabolic equations with suitable lower-order terms in homogenization, and the approximate two-sphere one-cylinder inequality continues to hold. The difficulty is to handle the more “worse" junior coefficients in parabolic homogenization. The results obtained in the paper can be easily extended to the elliptic case, which are also new in elliptic homogenization.

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来源期刊

Annali di Matematica Pura ed Applicata 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it). A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.