On mappings with bounded distortion of triangles
Year: 2025
Type: article
Abstract: The article introduces a characteristic of a triangle, reflecting the measure of its nondegeneracy. The importance of studying this quantity is associated with the construction of highquality computational grids. It is shown that if a Sobolev class mapping distorts this characteristic multiple times, then this mapping is a mapping with limited distortion. In addition, it is proved that if the above condition and additionally the condition of limited distortion of the area of the triangle are satisfied, then the mapping is bi-Lipschitz. The article establishes estimates for all constants characterizing the mappings under study.
Source: Russian Mathematics
Author: V. A. Klyachin
Institution: Novosibirsk State University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4415079972