Gradient flows in shape optimization theory

DOI10.1134/s1064562423700990OpenAlexW4388021830MaRDI QIDQ6123096

P. I. Plotnikov, Jan Sokolowski

Publication date: 4 March 2024

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562423700990

zbMATH Keywords

inverse problemsshape optimizationEuler elasticaKohn-Vogelius functionalWillmore flow

Mathematics Subject Classification ID

Inverse problems in equilibrium solid mechanics (74G75) Inverse problems for PDEs (35R30) Optimization of shapes other than minimal surfaces (49Q10) Inverse problems in optimal control (49N45)

Cites Work

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• \(L^2\)-flow of elastic curves with clamped boundary conditions
• A Willmore-Helfrich \(L^2\)-flow of curves with natural boundary conditions
• An optimal design problem with perimeter penalization
• Elliptic equations with transmission and Wentzell boundary conditions and an application to steady water waves in the presence of wind
• Evolution of Elastic Curves in $\Rn$: Existence and Computation
• Optimal approximations by piecewise smooth functions and associated variational problems
• Determining conductivity by boundary measurements
• Shape Methods for the Transmission Problem with a Single Measurement

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