Integral inequalities on domains of the Euclidean space for functions with non-zero traces
Year: 2025
Type: article
Abstract: On plane and space domains, we present several integral inequalities for functions with non-zero boundary trace. These new inequalities for functions are generalizations of the isoperimetric inequalities from the author’s recent paper (F.G. Avkhadiev. An analog of the Poincaré metric and isoperimetric constants, Russian Mathematics, 2024, Vol. 68, No. 9, pp. 79–85). Our theorems are formulated using hyperbolic type domains, the distance from a point to the boundary of a domain and the hyperbolic radius. We give schemes of proofs using the Poincaré metric and its properties, some hyperbolic characteristics of plane domains as well as space domains of hyperbolic type in the sense of Loewner and Nirenberg.
Source: Russian Mathematics
Author: F. G. Avkhadiev
Institution: Kazan Federal University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4410728488