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MICROLOCAL REGULARITY FOR MIZOHATA TYPE DIFFERENTIAL OPERATORS

Part of: Holomorphic functions of several complex variables Partial differential equations General first-order equations and systems

Published online by Cambridge University Press:  27 September 2018

G. Hoepfner Open the ORCID record for G. Hoepfner [Opens in a new window]  and
R. Medrado
G. Hoepfner
Affiliation:
Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP, 13565-905, Brasil (hoepfner@dm.ufscar.br)
R. Medrado
Affiliation:
Universidade Federal do Ceará, Sobral, CE, Rua Estanislau Frota, 563, 62010-560, Brasil (renanmedrado@sobral.ufc.br)
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Abstract

We investigate interesting connections between Mizohata type vector fields and microlocal regularity of nonlinear first-order PDEs, establishing results in Denjoy–Carleman classes and real analyticity results in the linear case.

Keywords

wave front setFBI transformmicrolocal regularity

MSC classification

Primary: 35F30: Boundary value problems for nonlinear first-order equations 35A18: Wave front sets
Secondary: 35A20: Analytic methods, singularities 35B65: Smoothness and regularity of solutions 32A55: Singular integrals
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 4 , July 2020 , pp. 1185 - 1209
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Copyright
© Cambridge University Press 2018

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Footnotes

The work was supported in part by CAPES (grant number 2013/0224), CNPq (grant number 305746/2015-4) and FAPESP (grant numbers 2017/03825-1 and 2017/06993-2).

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