Hypoellipticity of a second order operator with a principal symbol changing sign across a smooth hypersurface
We give sufficient conditions for hypoellipticity of a second order operator with real-valued infinitely differentiable coefficients whose principal part is the product of a real-valued infinitely differentiable function φ(<i>x</i>) and the sum of squares of first order operators <i>X</i><sub>1</sub>,…,<i>X</i><sub><i>r</i></sub>. These conditions are related to the way in which φ(<i>x</i>) changes its sign, and the rank of the Lie algebra generated by φ<i>X</i><sub>1</sub>,…,φ<i>X</i><sub><i>r</i></sub> and <i>X</i><sub>0</sub> where <i>X</i><sub>0</sub> is the first order term of the operator. Our result is an extension of that of [<b>4</b>], and it includes some cases not treated in [<b>1</b>], [<b>5</b>] and [<b>8</b>].
- Journal of the Mathematical Society of Japan
Journal of the Mathematical Society of Japan 58(4), 1037-1077, 2006-10-01
The Mathematical Society of Japan