Research Description

My research focuses on Mathematical Analysis, particularly in the interplay between Hamiltonian systems, Differential Geometry, and Variational Methods. I am interested in the application of Critical Point Theory and Geometric Analysis to the study of dynamical systems, optimal trajectories, and the structure of solutions to partial differential equations arising in geometry and physics.

Recently, I have been working on the Allen-Cahn equation and related variational models, particularly in the context of Riemannian manifolds with boundary. My research explores the multiplicity of solutions, phase transition phenomena, and their connections to geometric measure theory and minimal surfaces. Another research directions is the study of Hamiltonian systems, with particular attention to the existence of brake orbits and variational principles governing their behavior.

Publications Overview

Source Total Papers Citations

🔗 Scopus 26 112
🔗 Google-Scholar 35 158
🔗 Preprints   4
(The citation count is updated periodically)

List of publications

Mathematical Analysis

• J.H. Andrade, D. Corona, S. Nardulli, P. Piccione, R. Ponciano “From bubbles to clusters: Multiple solutions to the Allen--Cahn system”, Preprint, 2024
  🔗 arXiv:2410.17026

• D. Corona, R. Giambò, P. Piccione, “A note on the regularity and the existence of Riemannian splines”, Preprint, 2024
  🔗 arXiv:2407.18408

• D. Corona, A. Della Corte, M. Farotti, “Dynamical properties of critical exponent functions”, Preprint, 2024
  🔗arXiv:2406.14487

• D. Corona, S. Nardulli, R. Oliver-Bonafoux, G. Orlandi, P. Piccione, “Multiplicity results for mass constrained Allen-Cahn equations on Riemannian manifolds with boundary”, Preprint, 2024
  🔗arXiv:2401.17847 

1. D. Corona, R. Giambò, “Global Models of Collapsing Scalar Field: Endstate”, Symmetry, 16(5), 583, 2024
   🔗 doi: 10.3390/sym16050583

2. D. Corona, R. Giambò, O. Luongo, “Motion of test particles in quasi anti-de Sitter regular black holes”, International Journal of Geometric Methods in Modern Physics, 2024
   🔗 doi: 10.1142/S021988782440019X

3. E. Caponio, D. Corona, R. Giambò, P. Piccione, “Fixed energy solutions to the Euler-Lagrange equations of an indefinite Lagrangian with affine Noether charge”, Annali di Matematica Pura e Applicata, 2024
   🔗 doi: 10.1007/s10231-024-01424-4

4. V. Benci, D. Corona, S. Nardulli, L. E. Osorio Acevedo, P. Piccione, “Corrigendum to: Lusternik-Schnirelman and Morse Theory for the Van der Waals-Cahn-Hilliard equation with volume constraint”, Nonlinear Analysis, vol. 238, 2024
   🔗 doi: 10.1016/j.na.2023.113389

5. D. Corona, A. Della Corte, “Mixing properties of erasing interval maps”, Ergodic Theory and Dynamical Systems, vol. 44(2), 2024
   🔗 doi: 10.1017/etds.2023.16

6. D. Corona, A. Della Corte, F. Giannoni, “A non-autonomous variational problem describing a non-linear Timoshenko beam”, SIAM Journal of Mathematical Analysis, vol. 55(5), 2023
   🔗 doi: 10.1137/22M1493653

7. D. Corona, R. Giambò, F. Giannoni, P. Piccione, “On the relative category in the brake orbits problem”, Topological Methods in Nonlinear Analysis, vol. 61, no. 1, pp. 199-215, 2023
   🔗 doi: 10.12775/TMNA.2022.057

8. E. Caponio, D. Corona, “A variational setting for an indefinite Lagrangian with an affine Noether charge”, Calculus of Variations and Partial Differential Equations, 62:39, 2023
   🔗 doi: 10.1007/s00526-022-02379-1

9. D. Corona, F. Giannoni, “Brake orbits for Hamiltonian systems of classical type via Finsler geodesics”, Advances in Nonlinear Analysis, vol. 11, no. 1, 2022, pp. 1223-1248, 2022
   🔗 doi: 10.1515/anona-2022-0222

10. D. Corona, A. Della Corte, “The critical exponent functions”, Comptes Rendus Mathématique, vol. 360, pp. 315-332, 2022
    🔗 doi: 10.5802/crmath.286

11. D. Corona, “A multiplicity result for orthogonal geodesic chords in Finsler disks”, Discrete and Continuous Dynamical Systems, vol. 41(11), 2021
    🔗 doi: 10.3934/dcds.2021079

12. D. Corona, “A multiplicity result for Euler–Lagrange orbits satisfying the conormal boundary conditions”, Journal of Fixed Point Theory and Applications, vol. 22, pag. 60, 2020
    🔗 doi: 10.1007/s11784-020-00795-4

13. D. Corona and F. Giannoni, “A New Approach for Euler-Lagrange Orbits on Compact Manifolds with Boundary”, Symmetry, vol. 12, n. 11, pag. 1917, 2020
    🔗 doi: 10.3390/sym12111917

Control Theory

In the earlier years of my academic career, I worked on Optimal Control Theory, focusing on stability conditions and necessary optimality conditions for controlled dynamical systems. 

1. M. L. Corradini, G. Ippoliti, G. Orlando, D. Corona, “A data-driven model-free adaptive controller with application to wind turbines”, ISA Transactions, vol. 136, pp. 267–274, 2023
   🔗 doi: 10.1016/j.isatra.2022.11.002

2. D. Corona, A. Cristofaro, and D. Rotondo, “Reachability and stabilization of scheduled steady-states for LPV single-input systems”, Journal of the Franklin Institute, vol. 356, n. 8, pagg. 4478–4495, 2019
   🔗 doi: 10.1016/j.jfranklin.2019.04.007

3. D. Corona and A. Cristofaro, “Optimality principles and decomposition of tracking controllers for weakly dual redundant systems”, Optimal Control Applications and Methods,16, 2018
   🔗 doi: 10.1002/oca.2420

4. D. Corona and A. Cristofaro, “Optimal controlled steady-states for multi-input underactuated systems”, 18th European Control Conference (ECC), 3734-3739, 2019
   🔗 doi: 10.23919/ECC.2019.8795796

5. D. Corona and A. Cristofaro, "Optimal closed-loop tracking controllers for weakly dual redundant systems with periodic references", IEEE CDC, 2018
   🔗 doi: 10.1109/CDC.2018.8619169

6. D. Corona and A. Cristofaro, and D. Rotondo, “Optimizing output regulation for a class of underactuated LPV systems”, in Mediterranean control conference, pagg. 135–140, 2017
   🔗 doi: 10.1109/MED.2017.7984107

7. D. Corona and A. Cristofaro, and M. L. Corradini, “Optimal output regulation for underactuated systems with quasiperiodic references”, IFAC World Congress 2017, pagg. 3717–3722, 2017
   🔗 doi: 10.1016/j.ifacol.2017.08.712

8. D. Corona and A. Cristofaro, “Some remarks on optimal output regulation for weakly dual redundant plants”, in Mediterranean control conference, pagg. 1205–1211, 2016
   🔗 doi: 10.1109/MED.2016.7536028

Gesture Recognition

I have been involved in Gesture Recognition research, applying mathematical tools from analysis and geometry to develop efficient models for recognizing complex motion patterns.

1. F. Pezzuoli, D. Corona, and M. L. Corradini, “Recognition and classification of dynamic hand gestures by a wearable data-glove”, SN Computer Science, vol. 2, 2021
   🔗 doi: 10.1007/s42979-020-00396-5

2. F. Pezzuoli, D. Tafaro, M. Pane, D. Corona, and M. L. Corradini, “Development of a new sign language translation system for people with autism spectrum disorder”, Advances in Neurodevelopmental Disorders, 2020
   🔗 doi: 10.1007/s41252-020-00175-6

3. F. Pezzuoli, D. Corona, and M. L. Corradini, “Dynamic gestures recognition through a low-cost data glove”, in 2020 IEEE international conference on human-machine systems (ICHMS), pagg. 1–3, 2020
   🔗 doi: 10.1109/ICHMS49158.2020.9209424

4. F. Pezzuoli, D. Corona, and M. L. Corradini, “Improvements in a Wearable Device for Sign Language Translation”, in Advances in Human Factors in Wearable Technologies and Game Design, AHFE, pagg. 70–81, 2019
   🔗 doi: 10.1007/978-3-030-20476-1_9

5. F. Pezzuoli, D. Corona, M. L. Corradini, and A. Cristofaro, “Development of a wearable device for sign language translation”, in Int. Workshop on human-friendly robotics (HFR2017), Cham, pagg. 115–126, 2017
   🔗 doi: 10.1007/978-3-319-89327-3_9

List of collaborators

I would like to express my gratitude to all the authors, and friends, who have collaborated with me in my (or, better, their) research publications.
The list of authors is as follows (in alphabetical order):

• João Henrique de Andrade

• Vieri Benci

• Erasmo Caponio

• Andrea Cristofaro

• Letizia Corradini

• Alessandro Della Corte

• Marco Farotti

• Roberto Giambò

• Fabio Giannoni

• Orlando Luongo

• Stefano Nardulli

• Ramon Oliver-Bonafoux

• Giandomenico Orlandi

• Luis Edoardo Osorio Acevedo

• Francesco Pezzuoli

• Paolo Piccione

• Raoní Ponciano

• Damiano Rotondo