Regularity properties of free discontinuity sets

DOI10.1016/S0294-1449(01)00078-6zbMath1024.49013OpenAlexW2004138721MaRDI QIDQ5953873

Sergio Solimini, Francesco Maddalena

Publication date: 5 June 2002

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2001__18_6_675_0

zbMATH Keywords

regularityminimizationMumford-Shah functional

Mathematics Subject Classification ID

Regularity of solutions in optimal control (49N60) Existence theories for free problems in two or more independent variables (49J10) Methods involving semicontinuity and convergence; relaxation (49J45)

Related Items (9)

Higher integrability for the gradient of Mumford-Shah almost-minimizers ⋮ Some remarks on the analyticity of minimizers of free discontinuity problems. ⋮ Unnamed Item ⋮ Endpoint regularity for \(2d\) Mumford-Shah minimizers: on a theorem of Andersson and Mikayelyan ⋮ Density lower bound estimate for local minimizer of free interface problem with volume constraint ⋮ Higher integrability for minimizers of the Mumford-Shah functional ⋮ A regularity result for minimal configurations of a free interface problem ⋮ Unnamed Item ⋮ A selective review on Mumford-Shah minimizers

Cites Work

• Existence theory for a new class of variational problems
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• Simplified excision techniques for free discontinuity problems in several variables
• Existence theorem for a minimum problem with free discontinuity set
• Blow-up techniques and regularity near the boundary for free discontinuity problems
• Optimal approximations by piecewise smooth functions and associated variational problems
• $C^{1} $-Arcs for Minimizers of the Mumford-Shah Functional
• Lower semicontinuity properties of functionals with free discontinuities
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