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 $$sup_{int_D heta,dx=m} inf_{uin H^1_0(D)}int_DBig(rac{1+ heta}{2}| abla u|^2-fuBig),dx.$$ We prove the existence of an optimal reinforcement $ heta$ and that it has some higher integrability properties. We also provide some numerical computations for $ heta$ and $u$.
A free boundary problem arising in PDE optimization
BUTTAZZO, GIUSEPPE;Bozhidar Velichkov
2015-01-01
Abstract
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 $$sup_{int_D heta,dx=m} inf_{uin H^1_0(D)}int_DBig(rac{1+ heta}{2}| abla u|^2-fuBig),dx.$$ We prove the existence of an optimal reinforcement $ heta$ and that it has some higher integrability properties. We also provide some numerical computations for $ heta$ and $u$.File in questo prodotto:
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