Extremal p -Laplacian eigenvalues

Antunes, Pedro R. S.

http://hdl.handle.net/10400.2/9685

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Authors

Antunes, Pedro R. S.

Abstract(s)

We 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.