Реферат: The problem of identifying an inclusion is considered. The inclusion is an unknown subdomain of a given physical region. Available information on the inclusion is given by measurements on the boundary of this region. This class of problems includes single-measurement electrical impedance tomography and other inverse problems. The shape identification problem can be solved by minimizing an objective function characterizing the deviation of a given configuration from an admissible solution of the problem. The best choice of such an objective function is the Kohn–Vogelius energy functional. The standard regularization of the Kohn–Vogelius functional is considered, which is obtained by adding to the functional a linear combination of the perimeter of the inclusion and the Willmore curvature functional evaluated for an admissible inclusion boundary. In the two-dimensional case, a nonlocal theorem on the existence of strong solutions is proved for the gradient flow dynamical system generated for such a regularization of the Kohn–Vogelius functional

Библиографическая ссылка: П. И. Плотников , Jan Sokołowski
Gradient Flows in Shape Optimization Theory
Doklady Mathematics. 2023. N108. P.387–391. DOI: 10.1134/s1064562423700990 WOS Scopus РИНЦ OpenAlex

Даты:

Поступила в редакцию:	6 февр. 2023 г.
Принята к публикации:	7 авг. 2023 г.
Опубликована в печати:	30 окт. 2023 г.

Идентификаторы БД:

Web of science:	WOS:001097713700001
Scopus:	2-s2.0-85175267653
РИНЦ:	63935826
OpenAlex:	W4388021830

Цитирование в БД:

БД	Цитирований
OpenAlex	1
РИНЦ	1
Web of science	1

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