Ly, IdrissaSeck, Diaraf2021-07-202021-07-202006-10-11Ly, I., & Seck, D. (2006). Existence of solutions for the one-phase and the multi-layer free-boundary problems with the p-laplacian operator. <i>Electronic Journal of Differential Equations, 2006</i>(128), pp. 1-23.1072-6691https://hdl.handle.net/10877/14001By considering the p-laplacian operator, we show the existence of a solution to the exterior (resp interior) free boundary problem with non constant Bernoulli free boundary condition. In the second part of this article, we study the existence of solutions to the two-layer shape optimization problem. From a monotonicity result, we show the existence of classical solutions to the two-layer Bernoulli free-boundary problem with nonlinear joining conditions. Also we extend the existence result to the multi-layer case.Text23 pages1 file (.pdf)enAttribution 4.0 InternationalBernoulli free boundary problemStarshaped domainShape optimizationShape derivativeMonotonicityArticle