On smooth solutions of a class of almost hypoelliptic equations of constant strength - Ghazaryan, Haik; Margaryan, Vachagan (Eurasian Mathematical Journal, 2019)
In this paper we state a new theorem about smoothness of solutions of almost hypoelliptic and hypoelliptic by Burenkov equation P(x',D)u = 0, where the coefficients of the linear differential operator P(x,D) = P(x1, ..., xn, D1, ..., Dn) of uniformly constant strength depend only on the variables x' = (x1, ..., xk), k ≤ n: if the operator P(x', D) is hypoelliptic by Burenkov and almost hypoelliptic for any x'∈ Ek, then all the solutions of the differential equation P(x', D)u = 0 belonging to a certain weighted Sobolev class are infinitely differentiable functions.