含1-拉普拉斯算子的拟线性椭圆型问题的变分和近似解

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.1512/iumj.2022.71.8881

G. Figueiredo, M. Pimenta

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引用次数: 5

摘要

在本文中，我们使用两种不同的方法得到了涉及1−拉普拉斯算子的拟线性椭圆型问题的节点解。在第一篇文章中，我们开发了一种基于最小化能量泛函的方法，该方法与涉及R中的1 -拉普拉斯算子的问题相关，该问题在Nehari集的一个子集上，该子集只包含变号函数。在第二部分中，我们通过对与之相关的p−拉普拉斯问题的解序列的深入分析，得到了一个有界域上包含1−拉普拉斯算子的拟线性椭圆型问题的节点解。在这两种情况下，与涉及签署的解决办法的有关结果相比，出现了一些技术困难。

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Nodal solutions to quasilinear elliptic problems involving the 1-Laplacian operator via variational and approximation methods

In this work we use two different methods to get nodal solutions to quasilinear elliptic problems involving the 1−Laplacian operator. In the first one, we develop an approach based on a minimization of the energy functional associated to a problem involving the 1−Laplacian operator in R , on a subset of the Nehari set which contains just sign-changing functions. In the second part we obtain a nodal solution to a quasilinear elliptic problem involving the 1−Laplacian operator in a bounded domain, through a thorough analysis of the sequence of solutions of the p−Laplacian problem associated to it, as p → 1. In both cases, several technical difficulties appear in comparison with the related results involving signed solutions.

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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.