Shape derivative of the Cheeger constant

DOI10.1051/cocv/2014018zbMath1315.49018OpenAlexW2134200063MaRDI QIDQ5250288

Enea Parini, Nicholas Saintier

Publication date: 19 May 2015

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://www.esaim-cocv.org/10.1051/cocv/2014018/pdf

zbMATH Keywords

Cheeger constantshape derivative1-Laplacian

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (5)

On the strict monotonicity of the first eigenvalue of the 𝑝-Laplacian on annuli ⋮ Boundary variation method for the generalized Cheeger problem ⋮ Complete systems of inequalities relating the perimeter, the area and the Cheeger constant of planar domains ⋮ Existence and Symmetry results for some overdetermined free boundary problems ⋮ On the Cheeger inequality for convex sets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Cheeger constant of curved strips
• Estimates of the best Sobolev constant of the embedding of \(\mathrm{BV}(\Omega)\) into \(L^1(\partial \Omega)\) and related shape optimization problems
• Some remarks on uniqueness and regularity of Cheeger sets
• On a weighted total variation minimization problem
• Steklov eigenvalues for the \(\infty\)-Laplacian
• Area minimizing sets subject to a volume constraint in a convex set
• Characterization of Cheeger sets for convex subsets of the plane
• Variation and optimization of formes. A geometric analysis
• Stability and perturbations of the domain for the first eigenvalue of the 1-Laplacian
• On the perturbation of eigenvalues for the -Laplacian
• DIRICHLET PROBLEMS FOR THE 1-LAPLACE OPERATOR, INCLUDING THE EIGENVALUE PROBLEM
• Functions locally almost 1-harmonic
• THE DEPENDENCE OF THE FIRST EIGENVALUE OF THE INFINITY LAPLACIAN WITH RESPECT TO THE DOMAIN
• Uniqueness of the Cheeger set of a convex body

This page was built for publication: Shape derivative of the Cheeger constant