Year: 2025
Type: article
Abstract: We study Hardy-type inequalities with additional terms. The constant $\lambda(\Omega)$ multiplying the additional term depends on the geometry of the multidimensional domain $\Omega$ and the numerical parameters of the problem. This constant (functional) is commonly called the Brezis-Marcus constant. Avkhadiev and Wirths [1] put forward the conjecture that, over all $n$-dimensional domains with fixed inner radius $\delta_0$, the maximum best Brezis-Marcus constant is $\lambda(B_n)$, where $B_n $ is the $n$-ball of radius $\delta_0$. We improve the previously available lower estimates for $\lambda(B_n)$, for $n=2$ and $n= 4,…,10$, which takes us closer to this conjecture. Bibliography: 18 titles.
Source: Sbornik Mathematics
DOI: 10.4213/sm10120e
Author: Ramil' Gaisaevich Nasibullin
Institution: Kazan Federal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: Russian Science Foundation
Award: G8011563014
OpenAlex ID: W4411371505