@article{Iannizzotto2025, 
author = {Antonio Iannizzotto and Giovanni Porru},
title = {Optimization problems in rearrangement classes for fractional    p-Laplacian equations},
year = {2025},
journal = {Mathematics in Engineering},
volume = {7},
number = {1},
pages = {13-34},
keywords = {rearrangement class, fractional p-Laplacian, eigenvalues},
url = {https://www.sciopen.com/article/10.3934/mine.2025002},
doi = {10.3934/mine.2025002},
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 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.}
}