On the local solvability of a class of degenerate second order operators with complex coefficients

We study the local solvability of a class of operators with multiple characteristics. The class considered here complements and extends the one previously studied in Federico and Parmeggiani (CPDEs 2016, Vol. 41), in that in this paper we consider some cases of operators with complex coefficients that were not present in Federico and Parmeggiani. The class of operators considered here ideally encompasses classes of degenerate parabolic and Schrödinger type operators. We will give local solvability theorems. In general, one has L2 local solvability, but also cases of local solvability with better Sobolev regularity will be presented.