Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024698 | Nonlinear Analysis: Theory, Methods & Applications | 2017 | 24 Pages |
Abstract
We consider an optimization problem for the first Dirichlet eigenvalue of the p-Laplacian on a hypersurface in R2n, with nâ¥2. If pâ¥2nâ1, then among hypersurfaces in R2n which are O(n)ÃO(n)-invariant and have one fixed boundary component, there is a surface which maximizes the first Dirichlet eigenvalue of the p-Laplacian. This surface is either Simons' cone or a C1 hypersurface, depending on p and n. If n is fixed and p is large, then the maximizing surface is not Simons' cone. If p=2 and nâ¤5, then Simons' cone does not maximize the first eigenvalue.
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Authors
Sinan Ariturk,