Hypoellipticity for operators of infinitely degenerate Egorov type

Estimates and solvability

“…But it is still an open problem whether condition (q~) is sufficient for local solvability in three or more dimensions. For some other results on local solvability for principal type pseudo-differential operators, see [6], [7], [10], [13], [17] and [18].…”

Untitled

“…In [6], it was proved that operators on the form P = D t + iα(t)b(t, x, D x ) are hypoelliptic, where 0 ≤ α(t) ∈ C ∞ (R) only vanishes on intervals with Lebesgue measure zero, b(t, x, ξ) ∈ C ∞ (R, S 1 cl (R n )), t → σ(b)(t, x, ξ) is real and nondecreasing, and (τ, σ(b)) satisfies the Hörmander bracket condition; i.e., not all the Poisson brackets vanish. These operators generalize the microlocal models of the subelliptic operators.…”