Abstract:
We consider the optimization problem of minimizing ∫Ω | ∇ u |p d x with a constraint on the volume of { u > 0 }. We consider a penalization problem, and we prove that for small values of the penalization parameter, the constrained volume is attained. In this way we prove that every solution u is locally Lipschitz continuous and that the free boundary, ∂ { u > 0 } ∩ Ω, is smooth. © 2006 Elsevier Inc. All rights reserved.
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Citas:
---------- APA ----------
Fernández Bonder, J., Martínez, S. & Wolanski, N.
(2006)
. An optimization problem with volume constraint for a degenerate quasilinear operator. Journal of Differential Equations, 227(1), 80-101.
http://dx.doi.org/10.1016/j.jde.2006.03.006---------- CHICAGO ----------
Fernández Bonder, J., Martínez, S., Wolanski, N.
"An optimization problem with volume constraint for a degenerate quasilinear operator"
. Journal of Differential Equations 227, no. 1
(2006) : 80-101.
http://dx.doi.org/10.1016/j.jde.2006.03.006---------- MLA ----------
Fernández Bonder, J., Martínez, S., Wolanski, N.
"An optimization problem with volume constraint for a degenerate quasilinear operator"
. Journal of Differential Equations, vol. 227, no. 1, 2006, pp. 80-101.
http://dx.doi.org/10.1016/j.jde.2006.03.006---------- VANCOUVER ----------
Fernández Bonder, J., Martínez, S., Wolanski, N. An optimization problem with volume constraint for a degenerate quasilinear operator. J. Differ. Equ. 2006;227(1):80-101.
http://dx.doi.org/10.1016/j.jde.2006.03.006