Regularity and singularities of optimal convex shapes in the plane

DOI10.1007/s00205-012-0514-7zbMath1268.49051arXiv1112.3054OpenAlexW2033659705MaRDI QIDQ2276322

Jimmy Lamboley, Michel Pierre, Arian Novruzi

Publication date: 5 November 2012

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.3054

zbMATH Keywords

convex setsregularity of minimizersshape optimizationconvexity constraint

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (11)

Parametric shape optimization using the support function ⋮ Regularity in shape optimization under convexity constraint ⋮ Polygons as maximizers of Dirichlet energy or first eigenvalue of Dirichlet-Laplacian among convex planar domains ⋮ On minimizers of an isoperimetric problem with long-range interactions under a convexity constraint ⋮ An iterated projection approach to variational problems under generalized convexity constraints ⋮ A Transformation Approach in Shape Optimization: Existence and Regularity Results ⋮ Distributed and boundary expressions of first and second order shape derivatives in nonsmooth domains ⋮ Estimates of first and second order shape derivatives in nonsmooth multidimensional domains and applications ⋮ Elastic energy of a convex body ⋮ A reverse quantitative isoperimetric type inequality for the Dirichlet Laplacian ⋮ Blaschke--Santaló Diagram for Volume, Perimeter, and First Dirichlet Eigenvalue

Cites Work

• A family of inequalities for convex sets in the plane
• A Minkowski problem for electrostatic capacity
• Variation and optimization of formes. A geometric analysis
• The direct method in the calculus of variations for convex bodies
• On a long-standing conjecture by Pólya-Szegö and related topics
• Regularity of solutions for some variational problems subject to a convexity constraint
• Polygons as Optimal Shapes with Convexity Constraint
• On convex sets that minimize the average distance
• On the regularity of the solution of the Poisson problem on a domain with boundary locally similar to the boundary of a convex open set
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