Solvability of Planar Complex Vector Fields with Homogeneous Singularities

2012/09/28 by Abdelhamid Meziani, Meziani, Abdelhamid
Mathematics · #35A01 #35F05 (Primary) 35F15 (Secondary) #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Meromorphic and Entire Functions #advanced mathematical theories #math.AP #msc:35A01 #msc:35F05 #msc:35F15

paper · pdf · doi:10.48550/arxiv.1209.6613

arxiv created 2012/09/28 · openalex publication_date 2012/09/28 · arxiv updated 2012/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the equation Lu=f, where L is a \C-valued vector field in \R² with a homogeneous singularity. The properties of the solutions are linked to the number theoretic properties of a pair of complex numbers attached to the vector field.

Related

• On boundary properties of solutions of complex vector fields
• An F. and M. Riesz theorem for planar vector fields
• Global Solvability in Functional Spaces for Smooth Nonsingular Vector Fields in the Plane
• A strong uniqueness theorem for planar vector fields
• Feuilletages en droites, équations des eikonales et aures équations différentielles