非二重广义Orlicz空间中的Bloch估计

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-07-01 DOI:10.3934/mine.2023052

Petteri Harjulehto, P. Hasto, Jonne Juusti

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引用次数: 2

摘要

当$\varphi$具有广义Orlicz增长时，我们研究了非自治泛函\begin｛document｝$\begin{align*｝\inf\limits_u\int_\Omega\varphi（x，|\nabla u|）\，dx\end{align*}$\end｛document}的极小值。我们考虑$\varphi$的上增长率是无界的情况，并证明了极小值的Harnack不等式。我们的技术是基于“截断”函数$\varphi$来近似极小值，并通过近似极小值的Bloch估计使用一致常数进行Harnack估计。

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Bloch estimates in non-doubling generalized Orlicz spaces

We study minimizers of non-autonomous functionals

\begin{document}$ \begin{align*} \inf\limits_u \int_\Omega \varphi(x,|\nabla u|) \, dx \end{align*} $\end{document}

when $ \varphi $ has generalized Orlicz growth. We consider the case where the upper growth rate of $ \varphi $ is unbounded and prove the Harnack inequality for minimizers. Our technique is based on "truncating" the function $ \varphi $ to approximate the minimizer and Harnack estimates with uniform constants via a Bloch estimate for the approximating minimizers.

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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.