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math.AP2025
The Dirichlet problem for a family of totally degenerate differential operators
Maria Manfredini, Mirco Piccinini, Sergio Polidoro
In the framework of Potential Theory we prove existence or the Perron-Weiner-Brelot-Bauer solution to the Dirichlet problem related to a family of totally degenerate, in the sense…
math.AP2024
A study of the Kuramoto model for synchronization phenomena based on degenerate Kolmogorov-Fokker-Planck equations
Giulio Pecorella, Sergio Polidoro, Cecilia Vernia
We study a nonlinear partial differential equation that arises when introducing inertial effects in the Kuramoto model. Based on the known theory of degenerate Kolmogorov operators…