约翰域上改进的加权poincar不等式及其在散度方程中的应用

IF 0.4 4区数学 Q4 MATHEMATICS

Colloquium Mathematicum Pub Date : 2022-01-01 DOI:10.4064/cm8464-5-2021

M. E. Cejas

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引用次数: 0

摘要

．推广了文献[G]中关于poincar不等式和散度可解性的一些结果。阿科斯塔等人，安。学会科学。芬恩。数学，42(2017)]。更准确地说，我们将提供了支持加权改进庞卡罗不等式的权的充分条件的一般定理推广到无界约翰域。然后，我们应用这个不等式研究了散度方程在加权Sobolev空间中的可解性。因此，我们证明了权值大于a p的类在加权Sobolev空间中的可解性。

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Improved weighted Poincaré inequalities in John domains and application to the divergence equation

. We extend some results related to the Poincaré inequality and solvability of divergence obtained in [G. Acosta et al., Ann. Acad. Sci. Fenn. Math. 42 (2017)]. More precisely, we generalize to unbounded John domains the general theorem that provides a sufficient condition on a weight to support a weighted improved Poincaré inequality. Next, we apply this inequality to study the solvability of the divergence equation in weighted Sobolev spaces. As a consequence, we prove the solvability in weighted Sobolev spaces for weights in classes bigger than A p .

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来源期刊

Colloquium Mathematicum MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Colloquium Mathematicum is a journal devoted to the publication of original papers of moderate length addressed to a broad mathematical audience. It publishes results of original research, interesting new proofs of important theorems and research-expository papers in all fields of pure mathematics. Two issues constitute a volume, and at least four volumes are published each year.