Anatomy of the shape Hessian via Lie brackets

DOI10.1007/BF01783465zbMath0939.49023MaRDI QIDQ1817934

Dorin Bucur, Jean-Paul Zolésio

Publication date: 4 January 2000

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

zbMATH Keywords

shape optimizationLie bracketssymmetric bilinear formshape derivativeshape Hessian

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10) Applications of variational problems to control theory (58E25)

Related Items (8)

Shape derivatives in differential forms. I: An intrinsic perspective ⋮ On computation of the shape Hessian of the cost functional without shape sensitivity of the state variable ⋮ Shape derivatives for minima of integral functionals ⋮ Second order directional shape derivatives of integrals on submanifolds ⋮ Fixed point methods for internal free boundary problems ⋮ Distributed and boundary expressions of first and second order shape derivatives in nonsmooth domains ⋮ A Variational Method for Second Order Shape Derivatives ⋮ About stability of equilibrium shapes

Cites Work

• Anatomy of the shape Hessian
• Shape analysis via oriented distance functions
• Velocity Method and Lagrangian Formulation for the Computation of the Shape Hessian
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