Scholarly and Creative Works
2025
- Dipierro, S., Valdinoci, E., & Vaughan, M. C. (n.d.). A threshold for higher-order asymptotic development of genuinely nonlocal phase transition energies. Proceedings of the American Mathematical Society.
- Stinga, P. R., & Vaughan, M. C. (2025). Interior Schauder estimates for fractional elliptic equations in nondivergence form. SIAM Journal on Mathematical Analysis, 57.
- Patrizi, S., & Vaughan, M. C. (n.d.). The discrete dislocation dynamics of multiple dislocation loops. Archive for Rational Mechanics and Analysis, 249.
2024
- Delgadino, M. G., & Vaughan, M. C. (n.d.). Continuous symmetrizations and uniqueness of nonlocal equations. Analysis & PDE.
- Patrizi, S., & Vaughan, M. C. (2024). A convergence result for the derivation of front propagation in nonlocal phase field models. Interfaces and Free Boundaries.
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.
2020
- Stinga, P. R., & Vaughan, M. C. (2020). Fractional derivatives, fractional Laplacians, and weighted Sobolev spaces. Nonlinear Analysis, 193.
2019
- Aboud, A., Curl, E., Harding, S. N., Vaughan, M. C., & Weber, E. S. (2019). The dual Kaczmarz Algorithm. Acta Applicandae Mathematicae, 165.