International Journal of Differential Equations
- Int. J. Differ. Equ.
- Volume 2013 (2013), Article ID 526390, 8 pages.
Some Properties of Solutions to Weakly Hypoelliptic Equations
A linear different operator is called weakly hypoelliptic if any local solution of 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 -solution must vanish.
Int. J. Differ. Equ., Volume 2013 (2013), Article ID 526390, 8 pages.
Received: 21 May 2013
Accepted: 4 July 2013
First available in Project Euclid: 20 January 2017
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Bär, Christian. Some Properties of Solutions to Weakly Hypoelliptic Equations. Int. J. Differ. Equ. 2013 (2013), Article ID 526390, 8 pages. doi:10.1155/2013/526390. https://projecteuclid.org/euclid.ijde/1484881345