Blow-up of optimal sets in the irrigation problem

DOI10.1007/BF02922199zbMath1115.49029OpenAlexW1969337632MaRDI QIDQ2577093

Filippo Santambrogio, Paolo Tilli

Publication date: 3 January 2006

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02922199

zbMATH Keywords

regularity of minimizersblow-up limit\(H^1\)-constraintaverage distance functional

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Regularity of solutions in optimal control (49N60) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (11)

The average-distance problem with an Euler elastica penalization ⋮ The regularity of optimal irrigation patterns ⋮ The Average Distance Problem with Perimeter-to-Area Ratio Penalization ⋮ Counterexample to regularity in average-distance problem ⋮ Regularity for the Optimal Compliance Problem with Length Penalization ⋮ A presentation of the average distance minimizing problem ⋮ Long-term planningversusshort-term planning in the asymptotical location problem ⋮ Average-distance problem for parameterized curves ⋮ Partial regularity for the optimal \(p\)-compliance problem with length penalization ⋮ Approximation of Length Minimization Problems Among Compact Connected Sets ⋮ Where Best to Place a Dirichlet Condition in an Anisotropic Membrane?

Cites Work

• The structure of stationary one dimensional varifolds with positive density
• Convex analysis and measurable multifunctions
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