通过爆炸估计拉普拉斯的Lp值

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-06-02 DOI:10.1016/j.jde.2025.113478

Jan Lewenstein-Sanpera , Xavier Ros-Oton

引用次数: 0

摘要

在这篇文章中，我们提供了一个关于拉普拉斯函数的W2，p Calderón-Zygmund正则性估计的新证明，即Δu=f和它的抛物线对应的∂tu−Δu=f。我们的证明是一个矛盾性和紧性论证的改编，到目前为止，这个论证只被用来证明Hölder空间中的估计。这种新方法比以前的方法更简单，并且避免了使用任何插值定理。

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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Lp estimates for the Laplacian via blow-up

In this note we provide a new proof of the

W^{2, p}

Calderón-Zygmund regularity estimates for the Laplacian, i.e.,

Δ u = f

and its parabolic counterpart

\partial_{t} u - Δ u = f

. Our proof is an adaptation of a contradiction and compactness argument that so far had been only used to prove estimates in Hölder spaces. This new approach is simpler than previous ones, and avoids the use of any interpolation theorem.

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics