A free boundary problem arising in PDE optimization - Université Grenoble Alpes
Article Dans Une Revue Calculus of Variations and Partial Differential Equations Année : 2015

A free boundary problem arising in PDE optimization

Giuseppe Buttazzo
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Edouard Oudet
Bozhidar Velichkov

Résumé

A free boundary problem arising from the optimal reinforcement of a membrane or from the reduction of traffic congestion is considered; it is of the form $$\sup_{\int_D \theta dx=m} \inf_{u\in H_0^1(D)} \int_D \left(\frac{1 + \theta}2 |\nabla u|^2 − f u\right) dx.$$ We prove the existence of an optimal reinforcement $\theta$ and that it has some higher integrability properties. We also provide some numerical computations for $\theta$ and $u$.
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Dates et versions

hal-02009504 , version 1 (06-02-2019)

Identifiants

Citer

Giuseppe Buttazzo, Edouard Oudet, Bozhidar Velichkov. A free boundary problem arising in PDE optimization. Calculus of Variations and Partial Differential Equations, 2015, 54 (4), pp.3829-3856. ⟨10.1007/s00526-015-0923-1⟩. ⟨hal-02009504⟩
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