A generalized Cauchy-Lipschitz theorem in low regularity spaces

2017/01/10 by Arnaud Heibig, Heibig, Arnaud
Mathematics · #12H20 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1701.02636

openalex publication_date 2017/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove well-posedness for some abstract differential equations of the first order. Our result covers the usual case of Lipschitz composition operators. It also contains the case of some integro-differential operators acting on spaces with low regularity indexes. The loss of derivatives induced by such operators has to be lower than one, in order to be dominated by the first order derivative involved in the problem.

Related

• A two spaces extension of Cauchy-Lipschitz Theorem
• Strictly Hyperbolic Equations with Coefficients Low-Regular in Time and Smooth in Space
• Convex integration for Lipschitz mappings and counterexamples to regularity
• The maximal regularity property of abstract integro-differential equations
• Lipschitz regularity for integro-differential equations with coercive Hamiltonians and application to large time behavior