Optimization problems in rearrangement classes for fractional $p$-Laplacian equations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910699648712704 |
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| author | Iannizzotto, Antonio Porru, Giovanni |
| author_facet | Iannizzotto, Antonio Porru, Giovanni |
| contents | 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 maximization 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_10088 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimization problems in rearrangement classes for fractional $p$-Laplacian equations Iannizzotto, Antonio Porru, Giovanni Analysis of PDEs 35R11, 35P30 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 maximization 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. |
| title | Optimization problems in rearrangement classes for fractional $p$-Laplacian equations |
| topic | Analysis of PDEs 35R11, 35P30 |
| url | https://arxiv.org/abs/2411.10088 |