Antunes, Pedro R. S.2020-05-112020-05-112019-110951-7715http://hdl.handle.net/10400.2/9685We study the shape optimization problem of variational Dirichlet and Neumann p-Laplacian eigenvalues, with area and perimeter constraints. We prove some results that characterize the optimizers and derive the formula for the Hadamard shape derivative of Neumann p-Laplacian eigenvalues. Then, we propose a numerical method based on the radial basis functions method to solve the eigenvalue problems associated to the p-Laplacian operator. Several numerical results are presented and some new conjectures are addressed.engp-LaplacianEigenvaluesShape optimizationjournal article10.1088/1361-6544/ab47c51361-6544