Global solvability and global hypoellipticity for a class of complex vector fields on the 3-torus
Journal of Pseudo-Differential Operators and Applications, 2015•Springer
This work deals with global solvability and global hypoellipticity of complex vector fields of
the form L= ∂/∂ t+ ib_1 (t) ∂/∂ x_1+ ib_2 (t) ∂/∂ x_2 L=∂/∂ t+ ib 1 (t)∂/∂ x 1+ ib 2
(t)∂/∂ x 2, defined on T^ 3 ≃ R^ 3/2 π Z^ 3 T 3≃ R 3/2 π Z 3, where both b_1 b 1 and b_2 b
2 belong to C^ ∞ (T^ 1; R). C∞(T 1; R). The solvability and hypoellipticity depend on
condition (\mathcal PP) and also on Diophantine properties of the coefficients.
the form L= ∂/∂ t+ ib_1 (t) ∂/∂ x_1+ ib_2 (t) ∂/∂ x_2 L=∂/∂ t+ ib 1 (t)∂/∂ x 1+ ib 2
(t)∂/∂ x 2, defined on T^ 3 ≃ R^ 3/2 π Z^ 3 T 3≃ R 3/2 π Z 3, where both b_1 b 1 and b_2 b
2 belong to C^ ∞ (T^ 1; R). C∞(T 1; R). The solvability and hypoellipticity depend on
condition (\mathcal PP) and also on Diophantine properties of the coefficients.
Abstract
This work deals with global solvability and global hypoellipticity of complex vector fields of the form , defined on , where both and belong to The solvability and hypoellipticity depend on condition () and also on Diophantine properties of the coefficients.
Springer
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