Gradient Flows in Shape Optimization Theory

• Published in: Doklady. Mathematics Vol. 108; no. 2; pp. 387 - 391
• Main Authors: Plotnikov, P. I., Sokolowski, J.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.10.2023; Springer Nature B.V
• Subjects: Electrical impedance; Existence theorems; Gradient flow; Inverse problems; Mathematics; Mathematics and Statistics; Regularization; Shape optimization; Euler elastica; shape optimization; Willmore flow; inverse problems

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...