Geodesic
Isoperimetric inequality for an interior free boundary problem with \(p\)-Laplacian operator
Electronic journal of differential equations, Tome 2004 (2004)
By considering the p-Laplacian operator, we establish an existence and regularity result for a shape optimization problem. From a monotony result, we show the existence of a solution to the interior problem with a free surface for a family of Bernoulli constants. We also give an optimal estimation for the upper bound of the Bernoulli constant.
Classification : 35R35
Keywords: Bernoulli free boundary problem, starshaped domain, shape optimization, shape derivative, monotony 
@article{EJDE_2004__2004__a179,
     author = {Ly,  Idrissa and Seck,  Diaraf},
     title = {Isoperimetric inequality for an interior free boundary problem with {\(p\)-Laplacian} operator},
     journal = {Electronic journal of differential equations},
     year = {2004},
     volume = {2004},
     zbl = {1070.35137},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a179/}
}
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%A Seck,  Diaraf
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Ly,  Idrissa; Seck,  Diaraf. Isoperimetric inequality for an interior free boundary problem with \(p\)-Laplacian operator. Electronic journal of differential equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a179/