A free boundary problem related to thermal insulation

DOI10.1080/03605302.2016.1199038zbMath1351.35268arXiv1511.05934OpenAlexW2280614589MaRDI QIDQ2833274

Dennis Kriventsov, Luis A. Caffarelli

Publication date: 17 November 2016

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.05934

zbMATH Keywords

free boundary problemfree discontinuitiesthermal insulation

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Free boundary problems for PDEs (35R35)

Related Items (20)

An optimal insulation problem ⋮ Shape optimization of a thermal insulation problem ⋮ Existence and regularity of optimal shapes for spectral functionals with Robin boundary conditions ⋮ The calibration method for the thermal insulation functional ⋮ Minimization of the \(k\)-th eigenvalue of the Robin-Laplacian ⋮ An isoperimetric result for an energy related to the \(p\)-capacity ⋮ Higher integrability of the gradient for the thermal insulation problem ⋮ A free boundary problem for the \(p\)-Laplacian with nonlinear boundary conditions ⋮ An optimal design problem for a two-phase isolating material in the wall of a cavity ⋮ A two-phase problem with Robin conditions on the free boundary ⋮ On the honeycomb conjecture for Robin Laplacian eigenvalues ⋮ A free boundary problem related to thermal insulation: flat implies smooth ⋮ Numerical hints for insulation problems ⋮ The quantitative Faber-Krahn inequality for the Robin Laplacian ⋮ Optimal partitions for Robin Laplacian eigenvalues ⋮ Multiphase free discontinuity problems: monotonicity formula and regularity results ⋮ Degenerate free discontinuity problems and spectral inequalities in quantitative form ⋮ Best constant in Poincaré inequalities with traces: a free discontinuity approach ⋮ An optimization problem in thermal insulation with Robin boundary conditions ⋮ A free boundary problem in thermal insulation with a prescribed heat source

Cites Work

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• Singular sets of minimizers for the Mumford-Shah functional
• Existence theorem for a minimum problem with free discontinuity set
• Monotonicity formula and regularity for general free discontinuity problems
• Optimal approximations by piecewise smooth functions and associated variational problems

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