Optimization problems in rearrangement classes for fractional $ p $-Laplacian equations
We discuss two optimization problems related to the fractional $ p $-Laplacian. First, we prove the existence of at least one minimizer for the principal eigenvalue of the fractional $ p $-Laplacian with Dirichlet conditions, with a bounded weight function varying in a rearrangement class. Then, we...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-02-01
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| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2025002 |
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| Summary: | We discuss two optimization problems related to the fractional $ p $-Laplacian. First, we prove the existence of at least one minimizer for the principal eigenvalue of the fractional $ p $-Laplacian with Dirichlet conditions, with a bounded weight function varying in a rearrangement class. Then, we investigate the minimization of the energy functional for general nonlinear equations driven by the same operator, as the reaction varies in a rearrangement class. In both cases, we provide a pointwise relation between the optimizing datum and the corresponding solution. |
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| ISSN: | 2640-3501 |