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Volume 7, Issue 3
Hypoellipticity of Nonlinear Partial Differential Equations

Zhou Xiaofang

J. Part. Diff. Eq.,7(1994),pp.215-230

Published online: 1994-07

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  • Abstract
In this paper, we study the hypoellipticity problems for fully nonlinear panial differential equations of order m. For a solution u ∈ C^p_{loc}(Ω), if the linearized operator for the nonlinear equation on u satisfies some subelliptic conditions, we can deduce u ∈ C^∞(Ω) by using the paradifferential operator theory of J. -M. Bony.
  • Keywords

Hypoellipticity patadifferential operators pata-linearization parametrix

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COPYRIGHT: © Global Science Press

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@Article{JPDE-7-215, author = {Zhou Xiaofang}, title = {Hypoellipticity of Nonlinear Partial Differential Equations}, journal = {Journal of Partial Differential Equations}, year = {1994}, volume = {7}, number = {3}, pages = {215--230}, abstract = { In this paper, we study the hypoellipticity problems for fully nonlinear panial differential equations of order m. For a solution u ∈ C^p_{loc}(Ω), if the linearized operator for the nonlinear equation on u satisfies some subelliptic conditions, we can deduce u ∈ C^∞(Ω) by using the paradifferential operator theory of J. -M. Bony.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5683.html} }
TY - JOUR T1 - Hypoellipticity of Nonlinear Partial Differential Equations AU - Zhou Xiaofang JO - Journal of Partial Differential Equations VL - 3 SP - 215 EP - 230 PY - 1994 DA - 1994/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5683.html KW - Hypoellipticity KW - patadifferential operators KW - pata-linearization KW - parametrix AB - In this paper, we study the hypoellipticity problems for fully nonlinear panial differential equations of order m. For a solution u ∈ C^p_{loc}(Ω), if the linearized operator for the nonlinear equation on u satisfies some subelliptic conditions, we can deduce u ∈ C^∞(Ω) by using the paradifferential operator theory of J. -M. Bony.
Zhou Xiaofang. (1970). Hypoellipticity of Nonlinear Partial Differential Equations. Journal of Partial Differential Equations. 7 (3). 215-230. doi:
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