Hipoelipticidade global analítica e Gevrey de sublaplacianos sob condições Diofantinas

Abstract

In this dissertation we consider the problem of global Gevrey regularity for a class of partial differential operators in the form of a sum of squares of vector fields and we show that these operators are globally Gevrey hypoeliptic on the torus if and only if their coefficients satisfy a certain Diophantine condition.