Degenerate Free Discontinuity Problems and Spectral Inequalities in Quantitative Form

Bucur, Dorin; Giacomini, Alessandro; Nahon, Mickaël

doi:10.1007/s00205-021-01688-7

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The Penalized Problem: Proof Of Theorem1

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2022

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Cited by 3 publications

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“…This is a similar method as what was used in [8] to handle a similar function with (v) ∼ 2βcv near 0 for some constants c, β > 0.…”

Section: The Penalized Problem: Proof Of Theoremmentioning

confidence: 99%

Shape optimization of a thermal insulation problem

et al. 2022

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We study a shape optimization problem involving a solid $$K\subset {\mathbb {R}}^n$$ K ⊂ R n that is maintained at constant temperature and is enveloped by a layer of insulating material $$\Omega $$ Ω which obeys a generalized boundary heat transfer law. We minimize the energy of such configurations among all $$(K,\Omega )$$ ( K , Ω ) with prescribed measure for K and $$\Omega $$ Ω , and no topological or geometrical constraints. In the convection case (corresponding to Robin boundary conditions on $$\partial \Omega $$ ∂ Ω ) we obtain a full description of minimizers, while for general heat transfer conditions, we prove the existence and regularity of solutions and give a partial description of minimizers.

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“…This is a similar method as what was used in [8] to handle a similar function with (v) ∼ 2βcv near 0 for some constants c, β > 0.…”

Section: The Penalized Problem: Proof Of Theoremmentioning

confidence: 99%