Gevrey micro-regularity for solutions to first order nonlinear PDE

DOI10.1016/j.jde.2009.06.021zbMath1180.35024OpenAlexW1968212862MaRDI QIDQ842902

Gerson Petronilho, Rafael F. Barostichi

Publication date: 28 September 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2009.06.021

zbMATH Keywords

Gevrey approximate solutionsGevrey wave-front setnonlinear PDE of first order

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear first-order PDEs (35F20) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Wave front sets in context of PDEs (35A18)

Related Items (14)

Microglobal regularity and the global wavefront set ⋮ Characterization of Gevrey Regularity by a Class of FBI Transforms ⋮ Global \(L^q\)-Gevrey functions and their applications ⋮ Unnamed Item ⋮ Approximate solutions of vector fields and an application to Denjoy–Carleman regularity of solutions of a nonlinear PDE ⋮ A FOURIER-TYPE CHARACTERISATION FOR GEVREY VECTORS ON HYPO-ANALYTIC STRUCTURES AND PROPAGATION OF GEVREY SINGULARITIES ⋮ Unnamed Item ⋮ MICROLOCAL REGULARITY FOR MIZOHATA TYPE DIFFERENTIAL OPERATORS ⋮ FBI transform characterization of ultradifferentiablity on maximally real submanifolds ⋮ On microlocal analyticity and smoothness of solutions of first-order nonlinear PDEs ⋮ Denjoy-Carleman classes: boundary values, approximate solutions and applications ⋮ Existence of Gevrey approximate solutions for certain systems of linear vector fields applied to involutive systems of first-order nonlinear PDEs ⋮ Approximate solutions and micro-regularity in the Denjoy-Carleman classes ⋮ Global L^q Gevrey functions, Paley-Weiner theorems, and the FBI transform

Cites Work

• On microlocal analyticity of solutions of 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)
• Instability of the Cauchy-Kovalevskaya solution for a class of nonlinear systems
• An Extension Theorem of Whitney Type for Non Quasi-Analytic Classes of Functions
• On the Analyticity of Solutions of First-Order Nonlinear PDE
• Intermediate optimal gevrey exponents occur
• On the C ∞ Wave-Front Set of Solutions of First-Order Nonlinear PDE's
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