On a Shape Derivative Formula in the Brunn--Minkowski Theory

DOI10.1137/15M1015844zbMath1384.49033OpenAlexW2288335782MaRDI QIDQ2957560

Abdesslam Boulkhemair

Publication date: 26 January 2017

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1015844

zbMATH Keywords

convex setsshape optimizationsupport functionsshape derivativeBrunn-Minkowski theorygauge functions

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10)

Related Items (8)

A new numerical approach for solving shape optimization fourth-order spectral problems among convex domains ⋮ Complete systems of inequalities relating the perimeter, the area and the Cheeger constant of planar domains ⋮ On numerical study of constrained coupled shape optimization problems based on a new shape derivative method ⋮ On an effective approach in shape optimization problem for Stokes equation ⋮ On a numerical approach for solving some geometrical shape optimization problems in fluid mechanics ⋮ On a numerical shape optimization approach for a class of free boundary problems ⋮ On the Cheeger inequality for convex sets ⋮ Blaschke--Santaló Diagram for Volume, Perimeter, and First Dirichlet Eigenvalue

Cites Work

• Interior free boundary problems for the Laplace equation
• Minimizing the second eigenvalue of the Laplace operator with Dirichlet boundary conditions
• Variation and optimization of formes. A geometric analysis
• Convexity properties of solutions to some classical variational problems
• Convexity of free boundaries with bernoulli type boundary condition
• Notions of convexity
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