Singularities of Nonlinear Elliptic Systems

2012/05/31 by David R. Adams, J. Xiao, Jie Xiao
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Class (philosophy) #Geometry #Gravitational singularity #Hausdorff space #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Nonlinear system #Physics #Pure mathematics #Quadratic equation #Singularity #Type (biology) #math.AP #msc:35J48 #msc:42B37

paper · pdf · doi:10.1080/03605302.2013.766753

18 pages Communications in Partial Differential Equations

openalex publication_date 2013/01/30 · arxiv created 2013/05/07 · arxiv updated 2013/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Through Morrey's spaces (plus Zorko's spaces) and their potentials/capacities as well as Hausdorff contents/dimensions, this paper estimates the singular sets of nonlinear elliptic systems of the even-ordered Meyers-Elcrat type and a class of quadratic functionals inducing harmonic maps.

Citations

• Partial Differential Equations
• Conformally flat manifolds, Kleinian groups and scalar curvature
• On the solutions of quasi-linear elliptic partial differential equations
• On the Solutions of Quasi-Linear Elliptic Partial Differential Equations
• The Analysis of Harmonic Maps and their Heat Flows