Ly, Idrissa; Seck, Diaraf Isoperimetric inequality for an interior free boundary problem with \(p\)-Laplacian operator. (English) Zbl 1070.35137 Electron. J. Differ. Equ. 2004, Paper No. 109, 12 p. (2004). Summary: 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. Cited in 12 Documents MSC: 35R35 Free boundary problems for PDEs 35J70 Degenerate elliptic equations Keywords:Bernoulli free boundary problem; starshaped domain; shape optimization; shape derivative; monotony PDFBibTeX XMLCite \textit{I. Ly} and \textit{D. Seck}, Electron. J. Differ. Equ. 2004, Paper No. 109, 12 p. (2004; Zbl 1070.35137) Full Text: EuDML EMIS