INdAM-GNAMPA Project "Ottimizzazione spettrale non lineare" (Nonlinear spectral optimization)
Principal investigator: Dario Mazzoleni
Partecipants: Marco Degiovanni, Benedetta Pellacci, Berardo Ruffini, Gianmaria Verzini, Davide Zucco
Research topics:
1) Asymptotic problems for eigenvalues with weight arising from population dynamics
2) Optimization of the higher eigenvalues of the $p$-Laplacian for sign-changing capacitary measures
Papers with the support of the project:
1) V. Barutello, R. Ortega, G. Verzini, Regularized variational principles for the perturbed Kepler problem, preprint arXiv:2003.09383.
2) L. Brasco, D. Mazzoleni, On principal frequencies, volume and inradius in convex sets, Nonlinear Differ. Equ. Appl. 27, 12 (2020).
3) M. Degiovanni, M. Marzocchi, Quasilinear elliptic equations with natural growth and quasilinear elliptic equations with singular drift, Nonlinear Anal. 185 (2019), 206-215.
4) M. Degiovanni, D. Mazzoleni, Optimization results for the higher eigenvalues of the $p$-Laplacian associated with sign-changing capacitary measures, 104(1) (2021) , 97–146
5) S. Dipierro, B. Pellacci, E. Valdinoci, G. Verzini, Time-fractional equations with reaction terms: fundamental solutions and asymptotics, Discrete Cont. Dyn. Sys., 2021, 41(1), pp. 257–275
6) B. Pellacci, A. Pistoia, G. Vaira, G. Verzini, Normalized concentrating solutions to nonlinear elliptic problems, JDE, 2021, 275, pp. 882–919.
7) D. Pierotti, N. Soave, G. Verzini, Local minimizers in absence of ground states for the critical NLS energy on metric graphs, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 2021, 151(2), pp. 705–733.
The project ended on March 10th 2020. Some research collaborations partially supported by the grant are still ongoning.