5799
2012
eng
preprint
1
2012-07-06
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Some properties of solutions to weakly hypoelliptic equations
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.
urn:nbn:de:kobv:517-opus-60064
6006
RVK-Klassifikation: SI 990
Keine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Christian Bär
Preprints des Instituts für Mathematik der Universität Potsdam
1(2012)22
eng
uncontrolled
Hypoelliptic operators
eng
uncontrolled
hypoelliptic estimate
eng
uncontrolled
Montel theorem
eng
uncontrolled
Vitali theorem
eng
uncontrolled
Liouville theorem
Mathematik
Liouville theorems, Phragmén-Lindelöf theorems
Hypoelliptic equations
open_access
2012
Institut für Mathematik
Universität Potsdam
https://publishup.uni-potsdam.de/files/5799/premath22_2012.pdf