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Volume 3, Issue 2
Gevrey-hypoellipticity for a Class of Parabolic Type Operators

Chen Hua

J. Part. Diff. Eq.,3(1990),pp.63-76

Published online: 1990-03

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  • Abstract
This paper studies the micro-local version of the Gevrey-hypoellipticity for a class of parabolic type operator, ∂_t-a(t, x; D_s,) (a(t, x;D_s) (a(t, x; ξ) ∈ C^∞([0, T], S^m_{G^m}(R^n)) (m ≥ 1/s) is a Gevrey-pseudoanaiytic symbol of class s(s > 1)), and we obtain the following main result: Under the condition (I), the operator stated above is micro-local Gevrey-hypoelliptic. In order to prove our main result, the auther have used (α, β) method in this paper.
  • Keywords

Gevrey-hypoellipticity wave front set in Gevrey-class (&#945 &#946) method

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@Article{JPDE-3-63, author = {Chen Hua}, title = {Gevrey-hypoellipticity for a Class of Parabolic Type Operators}, journal = {Journal of Partial Differential Equations}, year = {1990}, volume = {3}, number = {2}, pages = {63--76}, abstract = { This paper studies the micro-local version of the Gevrey-hypoellipticity for a class of parabolic type operator, ∂_t-a(t, x; D_s,) (a(t, x;D_s) (a(t, x; ξ) ∈ C^∞([0, T], S^m_{G^m}(R^n)) (m ≥ 1/s) is a Gevrey-pseudoanaiytic symbol of class s(s > 1)), and we obtain the following main result: Under the condition (I), the operator stated above is micro-local Gevrey-hypoelliptic. In order to prove our main result, the auther have used (α, β) method in this paper.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5799.html} }
TY - JOUR T1 - Gevrey-hypoellipticity for a Class of Parabolic Type Operators AU - Chen Hua JO - Journal of Partial Differential Equations VL - 2 SP - 63 EP - 76 PY - 1990 DA - 1990/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5799.html KW - Gevrey-hypoellipticity KW - wave front set in Gevrey-class KW - (α KW - β) method AB - This paper studies the micro-local version of the Gevrey-hypoellipticity for a class of parabolic type operator, ∂_t-a(t, x; D_s,) (a(t, x;D_s) (a(t, x; ξ) ∈ C^∞([0, T], S^m_{G^m}(R^n)) (m ≥ 1/s) is a Gevrey-pseudoanaiytic symbol of class s(s > 1)), and we obtain the following main result: Under the condition (I), the operator stated above is micro-local Gevrey-hypoelliptic. In order to prove our main result, the auther have used (α, β) method in this paper.
Chen Hua. (1970). Gevrey-hypoellipticity for a Class of Parabolic Type Operators. Journal of Partial Differential Equations. 3 (2). 63-76. doi:
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