Gevrey regularity for a generalization of the Oleĭnik-Radkevič operator

The Gevrey hypoellipticity of a class of models generalizing the Oleĭnik-Radkevič operator is studied. Some partial regularity result is also given. It is studied the partial and microlocal regularity of the operatorL(t,x;Dt,Dx)=Dt2+∑j=1nt2(rj−1)Dxj2 on Ω, open neighborhood of the origin in Rn+1, where the rj's are positive integers such that r1