TY - JOUR
A2 - Zhang, Qi
AU - Bär, Christian
PY - 2013
DA - 2013/07/31
TI - Some Properties of Solutions to Weakly Hypoelliptic Equations
SP - 526390
VL - 2013
AB - A linear different operator L is called weakly hypoelliptic if any local solution u of Lu=0 is smooth. We allow for systems, that is, the coefficients may be matrices, not necessarily of square size. This is a huge class of important operators which coverall elliptic, overdetermined elliptic, subelliptic, and parabolic equations. We extend several classical theorems from complex analysis to solutions of any weakly hypoelliptic equation: the Montel theorem providing convergent subsequences, the Vitali theorem ensuring convergence of a given sequence, and Riemann's first removable singularity theorem. In the case of constant coefficients, we show that Liouville's theorem holds, any bounded solution must be constant, and any Lp-solution must vanish.
SN - 1687-9643
UR - https://doi.org/10.1155/2013/526390
DO - 10.1155/2013/526390
JF - International Journal of Differential Equations
PB - Hindawi Publishing Corporation
KW -
ER -