Scholarly and Creative Works
2026
- Dipierro, S., Valdinoci, E., & Vaughan, M. C. (2026). A threshold for higher-order asymptotic development of genuinely nonlocal phase transition energies. Proceedings of the American Mathematical Society. Retrieved from https://pubs.ams.org/PROC/0000-000-00/S0002-9939-2026-17371-9
2025
- Stinga, P. R., & Vaughan, M. C. (2025). Interior Schauder estimates for fractional elliptic equations in nondivergence form. SIAM Journal on Mathematical Analysis, 57. Retrieved from https://epubs.siam.org/doi/10.1137/24M1656335
- Delgadino, M. G., & Vaughan, M. C. (2025). Continuous symmetrizations and uniqueness of nonlocal equations. Analysis & PDE, 18(10), 2325–2366. Retrieved from https://msp.org/apde/2025/18-10/p01.xhtml
- Patrizi, S., & Vaughan, M. C. (2025). The discrete dislocation dynamics of multiple dislocation loops. Archive for Rational Mechanics and Analysis, 249. Retrieved from https://link.springer.com/article/10.1007/s00205-025-02108-w
2024
- Patrizi, S., & Vaughan, M. C. (2024). A convergence result for the derivation of front propagation in nonlocal phase field models. Interfaces and Free Boundaries. Retrieved from https://ems.press/journals/ifb/articles/14298262
2021
- Stinga, P. R., & Vaughan, M. C. (2021). Fractional elliptic equations in nondivergence form: definition, applications and Harnack inequality. Journal de Mathématiques Pures et Appliquées, 156. Retrieved from https://www.sciencedirect.com/science/article/pii/S0021782421001458
2020
- Stinga, P. R., & Vaughan, M. C. (2020). Fractional derivatives, fractional Laplacians, and weighted Sobolev spaces. Nonlinear Analysis, 193. Retrieved from https://www.sciencedirect.com/science/article/abs/pii/S0362546X19301257
2019
- Aboud, A., Curl, E., Harding, S. N., Vaughan, M. C., & Weber, E. S. (2019). The dual Kaczmarz Algorithm. Acta Applicandae Mathematicae, 165. Retrieved from https://link.springer.com/article/10.1007/s10440-019-00244-6