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 operator L ( t , x ; D t , D x ) = D t 2 + ∑ j = 1 n t 2 ( r j − 1 ) D x j 2 on Ω, open neighborhood of the origin in R n + 1 , where the r j ʹs are positive integers such that r 1 < r 2 < ⋯ < r n .