Volume 11, Issue 2
On Regularity for Solutions of Non-linear Equation with Constant Multiple Characteristic

Fangtong Wu

J. Part. Diff. Eq., 11 (1998), pp. 151-162.

Published online: 1998-11

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  • Abstract
In this paper we consider the propagation of microlocal regularity near constant multiple characteristic or a real solution u ∈ H^s (s > m + max{μ, 2} + \frac{n}{2})or non-linear partial differential equation F(x, u,…, ∂^βu,…)_{(|β|≤m)} = 0 We will prove that the microlocal regularity ncar constant multiple characteristic of the solution u will propagate along bicharacteristic with constant multiplicity μ and have loss of smoothness up to order μ - 1 under Levi condition.
  • Keywords

Constant multiple characteristic Levi condition paradifferential operator bicharacteristic para-linearization

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@Article{JPDE-11-151, author = {}, title = {On Regularity for Solutions of Non-linear Equation with Constant Multiple Characteristic}, journal = {Journal of Partial Differential Equations}, year = {1998}, volume = {11}, number = {2}, pages = {151--162}, abstract = { In this paper we consider the propagation of microlocal regularity near constant multiple characteristic or a real solution u ∈ H^s (s > m + max{μ, 2} + \frac{n}{2})or non-linear partial differential equation F(x, u,…, ∂^βu,…)_{(|β|≤m)} = 0 We will prove that the microlocal regularity ncar constant multiple characteristic of the solution u will propagate along bicharacteristic with constant multiplicity μ and have loss of smoothness up to order μ - 1 under Levi condition.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5562.html} }
TY - JOUR T1 - On Regularity for Solutions of Non-linear Equation with Constant Multiple Characteristic JO - Journal of Partial Differential Equations VL - 2 SP - 151 EP - 162 PY - 1998 DA - 1998/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5562.html KW - Constant multiple characteristic KW - Levi condition KW - paradifferential operator KW - bicharacteristic KW - para-linearization AB - In this paper we consider the propagation of microlocal regularity near constant multiple characteristic or a real solution u ∈ H^s (s > m + max{μ, 2} + \frac{n}{2})or non-linear partial differential equation F(x, u,…, ∂^βu,…)_{(|β|≤m)} = 0 We will prove that the microlocal regularity ncar constant multiple characteristic of the solution u will propagate along bicharacteristic with constant multiplicity μ and have loss of smoothness up to order μ - 1 under Levi condition.
Fangtong Wu . (2019). On Regularity for Solutions of Non-linear Equation with Constant Multiple Characteristic. Journal of Partial Differential Equations. 11 (2). 151-162. doi:
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