Rellich Type Inequalities with Weights in Plane Domains
- Authors: Avkhadiev F.G.1
-
Affiliations:
- Kazan Federal University
- Issue: Vol 39, No 5 (2018)
- Pages: 639-646
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/202165
- DOI: https://doi.org/10.1134/S1995080218050049
- ID: 202165
Cite item
Abstract
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.
About the authors
F. G. Avkhadiev
Kazan Federal University
Author for correspondence.
Email: avkhadiev47@mail.ru
Russian Federation, ul. Kremlevskaya 18, Kazan, 420008