Dirichlet和Neumann拉普拉斯算子的Leibniz规则

IF 0.4 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal Pub Date : 2019-05-08 DOI:10.2748/tmj.20211112

T. Iwabuchi

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引用次数: 1

摘要

我们研究了具有Dirichlet和Neumann边界条件的Sobolev空间中的双线性估计。揭示了在半空间情况下得到这种估计的最优正则性，这不仅与函数的光滑性有关，而且与边界行为有关。证明的关键是如何处理函数及其导数的边值。

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The Leibniz rule for the Dirichlet and the Neumann Laplacian

We study the bilinear estimates in the Sobolev spaces with the Dirichlet and the Neumann boundary condition. The optimal regularity is revealed to get such estimates in the half space case, which is related to not only smoothness of functions and but also boundary behavior. The crucial point for the proof is how to handle boundary values of functions and their derivatives.

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来源期刊

Tohoku Mathematical Journal 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Information not localized