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An optimization problem for the first eigenvalue of the ‐fractional Laplacian |
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| Abstract: | In this paper we analyze an eigenvalue problem related to the nonlocal p‐Laplace operator plus a potential. After reviewing some elementary properties of the first eigenvalue of these operators (existence, positivity of associated eigenfunctions, simplicity and isolation) we investigate the dependence of the first eigenvalue on the potential function and establish the existence of some optimal potentials in some admissible classes. |
| Keywords: | Optimization fractional laplacian nonlinear eigenvalues 35J92 35P30 49R05 |
