On microlocal analyticity and smoothness of solutions of first-order nonlinear PDEs

DOI10.1007/s00208-011-0638-3zbMath1298.35006OpenAlexW2044197496MaRDI QIDQ661296

Shiferaw Berhanu, Ziad Adwan

Publication date: 10 February 2012

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-011-0638-3

zbMATH Keywords

first-order nonlinear PDEsmicrolocal analyticity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear first-order PDEs (35F20) Wave front sets in context of PDEs (35A18)

Related Items (8)

Analyticity and Smoothness for a Class of First Order Nonlinear PDEs ⋮ Microglobal regularity and the global wavefront set ⋮ The FBI transforms and their use in microlocal analysis ⋮ Unnamed Item ⋮ On some systems of real or complex vector fields and their related Laplacians ⋮ Regular multi-types and the Bloom conjecture ⋮ MICROLOCAL REGULARITY FOR MIZOHATA TYPE DIFFERENTIAL OPERATORS ⋮ Global L^q Gevrey functions, Paley-Weiner theorems, and the FBI transform

Cites Work

• Approximate solutions and micro-regularity in the Denjoy-Carleman classes
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• Gevrey micro-regularity for solutions to first order nonlinear PDE
• A generalization of Borel's theorem and microlocal Gevrey regularity in involutive structures
• Calcul paradifférentiel précisé et applications à des équations aux dérivées partielles non semilinéaires. (Precise paradifferential calculus and applications to non-semilinear partial differential equations)
• Semirigid partial differential operators and microlocal analytic hypoellipticity
• Instability of the Cauchy-Kovalevskaya solution for a class of nonlinear systems
• Uniqueness in certain first-order nonlinear complex cauchy problems
• On analytic microlocal hypoellipticity of linear partial differential operators of principal type
• On the C ∞ Wave-Front Set of Solutions of First-Order Nonlinear PDE's
• An F. and M. Riesz theorem for planar vector fields
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