变指数Sobolev空间中与J.L.Lions引理的等价关系及其应用

IF 0.8 4区数学 数学研究 Pub Date : 2022-06-01 DOI:10.4208/jms.v55n3.22.05

J. Aramaki

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引用次数: 1

摘要

．我们考虑了J. L. Lions引理的W−m, p(·)版本的等价条件，其中p(·)是满足某些条件的可变指数。作为m = 0的应用，我们首先推导了Korn不等式，并进一步考虑了它与其他基本结果的关系。本文的目的之一是应用于麦克斯韦-斯托克斯型问题弱解的存在性。

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Equivalent Relations with the J. L. Lions Lemma in a Variable Exponent Sobolev Space and Their Applications

. We consider the equivalent conditions with W − m , p ( · ) -version of the J. L. Lions Lemma, where p ( · ) is a variable exponent satisfying some condition. As applications with m = 0, we ﬁrst derive the Korn inequality and furthermore, we consider the relation to other fundamental results. One of the purpose of this paper is an application to the existence of a weak solution for the Maxwell-Stokes type problem.

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数学研究 MATHEMATICS-

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1109

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