Sharp Regularity Estimates for a Singular Inhomogeneous (m, p)-Laplacian Equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-26 DOI:10.1007/s11118-024-10164-2

Pêdra D. S. Andrade, João Vitor da Silva, Giane C. Rampasso, Makson S. Santos

引用次数: 0

Abstract

In this paper, we investigate a class of doubly nonlinear evolutions PDEs. We establish sharp regularity for the solutions in Hölder spaces. The proof is based on the geometric tangential method and intrinsic scaling technique. Our findings extend and recover the results in the context of the classical evolution PDEs with singular signature via a unified treatment in the slow, normal and fast diffusion regimes. In addition, we provide some applications to certain nonlinear evolution models, which may have their own mathematical interest.

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奇异非均质 (m, p)- 拉普拉斯方程的尖锐正则估计值

在本文中，我们研究了一类双非线性演化 PDE。我们为荷尔德空间中的解建立了尖锐的正则性。证明基于几何切向法和本征缩放技术。我们的研究结果通过在慢速、正常和快速扩散状态下的统一处理，扩展并恢复了具有奇异特征的经典演化 PDEs 的结果。此外，我们还提供了某些非线性演化模型的应用，这些模型可能有其自身的数学意义。

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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.