Local Solvability For a Class of Partial Differential Operators With Double Characteristics

Abstract

A necessary and sufficient condition for local solvability is presented for the linear partial differential operators $-X^2-Y^2+ia(x)[X,Y]$ in ${\mathbf{R}}^3=\{(x,y,t)\}$, where $X={\partial }_x,Y={\partial }_y+x^k{\partial }_t$, and $a\in C^{\infty }({\mathbf{R}}^1)$ is real valued, for each positive integer $k$.

References in corpus (1)

• Infinite dimensional families of locally nonsolvable partial differential operators

Cited by in corpus (2)

• Infinite dimensional families of locally nonsolvable partial differential operators
• Hypoellipticity and loss of derivatives with Appendix Analyticity and loss of derivatives