Optimization problems in rearrangement classes for fractional p-Laplacian equations

2024/11/15 by Iannizzotto, Antonio, Porru, Giovanni
#35P30 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.10088

Abstract

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.

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