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September 2012 Subelliptic estimates for overdetermined systems of quadratic differential operators
Karel Pravda-Starov
Osaka J. Math. 49(3): 563-611 (September 2012).


We prove global subelliptic estimates for systems of quadratic differential operators. Quadratic differential operators are operators defined in the Weyl quantization by complex-valued quadratic symbols. In a previous work, we pointed out the existence of a particular linear subvector space in the phase space intrinsically associated to their Weyl symbols, called singular space, which rules a number of fairly general properties of non-elliptic quadratic operators. About the subelliptic properties of these operators, we established that quadratic operators with zero singular spaces fulfill global subelliptic estimates with a loss of derivatives depending on certain algebraic properties of the Hamilton maps associated to their Weyl symbols. The purpose of the present work is to prove similar global subelliptic estimates for overdetermined systems of quadratic operators. We establish here a simple criterion for the subellipticity of these systems giving an explicit measure of the loss of derivatives and highlighting the non-trivial interactions played by the different operators composing those systems.


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Karel Pravda-Starov. "Subelliptic estimates for overdetermined systems of quadratic differential operators." Osaka J. Math. 49 (3) 563 - 611, September 2012.


Published: September 2012
First available in Project Euclid: 15 October 2012

zbMATH: 1270.35206
MathSciNet: MR2993058

Primary: 35B65
Secondary: 35N10

Rights: Copyright © 2012 Osaka University and Osaka City University, Departments of Mathematics


Vol.49 • No. 3 • September 2012
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