TY - INPR
A1 - Bär, Christian
T1 - Some properties of solutions to weakly hypoelliptic equations
N2 - A linear differential operator L is called weakly hypoelliptic if any local solution u of Lu = 0 is smooth. We allow for systems, i.e. the coefficients may be matrices, not necessarily of square size. This is a huge class of important operators which covers all 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 L^p solution must vanish.
T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)22
KW - Hypoelliptic operators
KW - hypoelliptic estimate
KW - Montel theorem
KW - Vitali theorem
KW - Liouville theorem
Y1 - 2012
UR - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/5799
UR - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-60064
ER -