Abstract:
We consider the optimization problem of minimizing ∫Ω G (| ∇ u |) d x in the class of functions W1, G (Ω), with a constraint on the volume of {u > 0}. The conditions on the function G allow for a different behavior at 0 and at ∞. 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. © 2007 Elsevier Inc. All rights reserved.
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Citas:
---------- APA ----------
(2008)
. An optimization problem with volume constraint in Orlicz spaces. Journal of Mathematical Analysis and Applications, 340(2), 1407-1421.
http://dx.doi.org/10.1016/j.jmaa.2007.09.061---------- CHICAGO ----------
Martínez, S.
"An optimization problem with volume constraint in Orlicz spaces"
. Journal of Mathematical Analysis and Applications 340, no. 2
(2008) : 1407-1421.
http://dx.doi.org/10.1016/j.jmaa.2007.09.061---------- MLA ----------
Martínez, S.
"An optimization problem with volume constraint in Orlicz spaces"
. Journal of Mathematical Analysis and Applications, vol. 340, no. 2, 2008, pp. 1407-1421.
http://dx.doi.org/10.1016/j.jmaa.2007.09.061---------- VANCOUVER ----------
Martínez, S. An optimization problem with volume constraint in Orlicz spaces. J. Math. Anal. Appl. 2008;340(2):1407-1421.
http://dx.doi.org/10.1016/j.jmaa.2007.09.061