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math.AP2025
On a class of globally analytic Hypoelliptic operators with non-negative characteristic form
Nicholas Braun Rodrigues, Gregorio Chinni
The global analytic hypoellipticity is proved for a class of second order partial differential equations with non-negative characteristic form globally defined on the torus. The cl…
math.AP2023
Smooth and Gevrey Microlocal Hypoellipticity for a Class of Hypocomplex Tube Structures
Nicholas Braun Rodrigues
We prove a smooth and Gevrey- microlocal hypoellipticity result for a system of complex vector fields associated with a real-analytic locally integrable structure of tube type,…
math.AP2018
Approximate solutions of vector fields and an application to Denjoy-Carleman regularity of solutions of a nonlinear PDE
Nicholas Braun Rodrigues, Antonio V. da Silva
In this paper we study microlocal regularity of a solution of the equation \begin{equation*} u_t = f(x,t,u,u_x), \end{equation*} where is ultrad…