Sharp Morrey regularity theory for a fourth order geometrical equation

IF 1.2 4区数学 Q1 MATHEMATICS

Acta Mathematica Scientia Pub Date : 2024-03-01 DOI:10.1007/s10473-024-0202-3

引用次数: 0

Abstract

This paper is a continuation of recent work by Guo-Xiang-Zheng [10]. We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation $$\Delta^{2}u=\Delta(V\nabla u)+{\text{div}}(w\nabla u)+(\nabla\omega+F)\cdot\nabla u+f\qquad\text{in}B^{4},$$ under the smallest regularity assumptions of V, ω, ω, F, where f belongs to some Morrey spaces. This work was motivated by many geometrical problems such as the flow of biharmonic mappings. Our results deepens the L^p type regularity theory of [10], and generalizes the work of Du, Kang and Wang [4] on a second order problem to our fourth order problems.

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四阶几何方程的锐莫里正则理论

摘要本文是 Guo-Xiang-Zheng [10] 近期工作的延续。我们推导了四阶非均质 Lamm-Rivière 方程的弱解的尖锐 Morrey 正则理论 $$\Delta^{2}u=\Delta(V\nabla u)+{\text{div}}(w\nabla u)+(\nabla\omega+F)\cdot\nabla u+f\qquad\text{in}B^{4}、$$ 在 V, ω, ω, F 的最小正则假设下，其中 f 属于某个 Morrey 空间。这项工作的动机来自于许多几何问题，比如双谐波映射的流动。我们的结果深化了 [10] 的 Lp 型正则性理论，并将 Du、Kang 和 Wang [4] 在二阶问题上的工作推广到我们的四阶问题上。

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

Acta Mathematica Scientia 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

2614

审稿时长

6 months

期刊介绍： Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.