Sufficient conditions for local solvability of some degenerate PDO with complex subprincipal symbol

TL;DR

This paper establishes sufficient conditions involving the real and imaginary parts of the complex subprincipal symbol for the local solvability of a class of degenerate second order linear PDEs, ensuring L^2 to L^2 solvability.

Contribution

It provides new invariant conditions for local solvability of degenerate PDEs with complex subprincipal symbols, expanding understanding of their solvability criteria.

Findings

Identifies invariant conditions involving real and imaginary parts of the subprincipal symbol.

Proves local L^2 to L^2 solvability under these conditions.

Extends solvability results to a class of degenerate operators with complex symbols.

Abstract

We will show a local solvability result for a class of degenerate second order linear partial differential operators with a complex subprincipal symbol. Due to the form of the operators in the class the subprincipal symbol is invariantly defined and we shall give sufficient conditions for the local solvability to hold involving the real and the imaginary part of the latter. Under suitable conditions we will prove that the class under consideration is L^2 to L^2 locally solvable.