Local Boundedness for Minimizers of Anisotropic Functionals with Monomial Weights

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-29 DOI:10.1007/s10957-024-02432-3

Filomena Feo, Antonia Passarelli di Napoli, Maria Rosaria Posteraro

引用次数: 0

Abstract

We study the local boundedness of minimizers of non uniformly elliptic integral functionals with a suitable anisotropic \(p,q-\) growth condition. More precisely, the growth condition of the integrand function \(f(x,\nabla u)\) from below involves different \(p_i>1\) powers of the partial derivatives of u and some monomial weights \(|x_i|^{\alpha _i p_i}\) with \(\alpha _i \in [0,1)\) that may degenerate to zero. Otherwise from above it is controlled by a q power of the modulus of the gradient of u with \(q\ge \max _i p_i\) and an unbounded weight \(\mu (x)\). The main tool in the proof is an anisotropic Sobolev inequality with respect to the weights \(|x_i|^{\alpha _i p_i}\).

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具有单项权重的各向异性函数最小化的局部有界性

我们研究了具有合适的各向异性 \(p,q-\)增长条件的非均匀椭圆积分函数最小值的局部有界性。更准确地说，积分函数 \(f(x,\nabla u)\)的增长条件从下往上涉及 u 的偏导数的不同 \(p_i>1\) 次幂和一些单项式权重 \(|x_i|^{\alpha _i p_i}\) with \(\alpha _i \in [0,1)\) ，这些权重可能退化为零。否则，从上面看，它是由u的梯度模的q次方控制的，有\(q\ge \max _i p_i\)和一个无约束权重\(\mu (x)\)。证明的主要工具是关于权重 \(|x_i|^{\alpha _i p_i}\) 的各向异性 Sobolev 不等式。

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.