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On Mappings with Bounded Distortion of Triangles. / Klyachin, V. A.

In: Russian Mathematics, Vol. 69, No. 9, 4, 09.2025, p. 33-39.

Research output: Contribution to journal › Article › peer-review

Harvard

Klyachin, VA 2025, 'On Mappings with Bounded Distortion of Triangles', Russian Mathematics, vol. 69, no. 9, 4, pp. 33-39. https://doi.org/10.3103/s1066369x25700690

APA

Klyachin, V. A. (2025). On Mappings with Bounded Distortion of Triangles. Russian Mathematics, 69(9), 33-39. [4]. https://doi.org/10.3103/s1066369x25700690

Vancouver

Klyachin VA. On Mappings with Bounded Distortion of Triangles. Russian Mathematics. 2025 Sept;69(9):33-39. 4. doi: 10.3103/s1066369x25700690

Author

Klyachin, V. A. / On Mappings with Bounded Distortion of Triangles. In: Russian Mathematics. 2025 ; Vol. 69, No. 9. pp. 33-39.

BibTeX

@article{e9df34d079484e5dba2db43b22f54b77,
title = "On Mappings with Bounded Distortion of Triangles",
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 high-quality computational grids. It is shown that if a Sobolev class mapping distorts this characteristic multiple times, then this mapping is a mapping with bounded distortion. In addition, it is proved that if the above condition and additionally the condition of bounded 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.",
keywords = "ИСКАЖЕНИЕ ТРЕУГОЛЬНИКОВ, КВАЗИРЕГУЛЯРНОЕ ОТОБРАЖЕНИЕ, БИЛИПШИЦЕВО ОТОБРАЖЕНИЕ, DISTORTION OF TRIANGLES, QUASIREGULAR MAPPING, BI-LIPSCHITZ MAPPING",
author = "Klyachin, {V. A.}",
note = "Klyachin V. A. On Mappings with Bounded Distortion of Triangles // Russian Mathematics. – 2025. – Vol. 69. - No. 9. – P. 33-39. – DOI 10.3103/S1066369X25700690. – EDN LAHFUI. This work was supported by the Mathematical Center in Akademgorodok, agreement with the Ministry of Science and Higher Education of the Russian Federation no. 075-15-2025-349 dated April 29, 2025.",
year = "2025",
month = sep,
doi = "10.3103/s1066369x25700690",
language = "English",
volume = "69",
pages = "33--39",
journal = "Russian Mathematics",
issn = "1066-369X",
publisher = "Allerton Press Inc.",
number = "9",

}

RIS

TY - JOUR

T1 - On Mappings with Bounded Distortion of Triangles

AU - Klyachin, V. A.

N1 - Klyachin V. A. On Mappings with Bounded Distortion of Triangles // Russian Mathematics. – 2025. – Vol. 69. - No. 9. – P. 33-39. – DOI 10.3103/S1066369X25700690. – EDN LAHFUI. This work was supported by the Mathematical Center in Akademgorodok, agreement with the Ministry of Science and Higher Education of the Russian Federation no. 075-15-2025-349 dated April 29, 2025.

PY - 2025/9

Y1 - 2025/9

N2 - 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 high-quality computational grids. It is shown that if a Sobolev class mapping distorts this characteristic multiple times, then this mapping is a mapping with bounded distortion. In addition, it is proved that if the above condition and additionally the condition of bounded 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.

AB - 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 high-quality computational grids. It is shown that if a Sobolev class mapping distorts this characteristic multiple times, then this mapping is a mapping with bounded distortion. In addition, it is proved that if the above condition and additionally the condition of bounded 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.

KW - ИСКАЖЕНИЕ ТРЕУГОЛЬНИКОВ

KW - КВАЗИРЕГУЛЯРНОЕ ОТОБРАЖЕНИЕ

KW - БИЛИПШИЦЕВО ОТОБРАЖЕНИЕ

KW - DISTORTION OF TRIANGLES

KW - QUASIREGULAR MAPPING

KW - BI-LIPSCHITZ MAPPING

UR - https://www.scopus.com/pages/publications/105027749177

UR - https://www.elibrary.ru/item.asp?id=88811997

UR - https://www.elibrary.ru/item.asp?id=82969198

UR - https://www.mendeley.com/catalogue/8c217a9c-1fc4-3349-8bec-b22b0a321e39/

U2 - 10.3103/s1066369x25700690

DO - 10.3103/s1066369x25700690

M3 - Article

VL - 69

SP - 33

EP - 39

JO - Russian Mathematics

JF - Russian Mathematics

SN - 1066-369X

IS - 9

M1 - 4

ER -

ID: 74617103