David S. Tartakoff
Local Analytic Hypoellipticity for $D_x^2+D_y^2+(x^{2m}+y^{2n})D_t^2$
Preprint series: ESI preprints

MSC:

35H05 Hypoelliptic equations and systems, See also {58Gxx}

Abstract: We give a new and very simple proof of the local analytic
hypoellipticity of some partial
differential operators studied by Matzusawa in
\cite{Matzusawa 1986} and their generalizations. These
include the operator
$$\left( {{\partial} \over {\partial x}} \right)^2
+\left( {{\partial} \over {\partial y}} \right)^2
+ (x^{2m}+y^{2n})
\left( {{\partial} \over {\partial t}} \right)^2.$$
These operators represent a simple class which had not
yielded to the methods of Derridj and Tartakoff to date.

Keywords: local analytic hypoellipticity, partial differential operator