Rellich Type Inequalities with Weights in Plane Domains
- 作者: Avkhadiev F.1
-
隶属关系:
- Kazan Federal University
- 期: 卷 39, 编号 5 (2018)
- 页面: 639-646
- 栏目: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/202165
- DOI: https://doi.org/10.1134/S1995080218050049
- ID: 202165
如何引用文章
详细
We determine some special functionals as sharp constants in integral inequalities for test functions, defined on plane domains. First we prove a new one dimensional integral inequality. Also, we prove some generalizations of a classical Rellich result for two dimensional case, when there is an additional restriction for Fourier coefficients of the test functions. In addition, we examine a Rellich type inequality in plane domains with infinite Euclidean maximal modulus. As an application of our results we present a new simple proof of a remarkable theorem of P. Caldiroli and R. Musina from their paper “Rellich inequalities with weights”, published in Calc. Var. 45 (2012), 147–164.
作者简介
F. Avkhadiev
Kazan Federal University
编辑信件的主要联系方式.
Email: avkhadiev47@mail.ru
俄罗斯联邦, ul. Kremlevskaya 18, Kazan, 420008
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