Singularities of Nonlinear Elliptic Systems
David R. Adams, J. Xiao
TL;DR
This paper investigates the singularities of nonlinear elliptic systems of Meyers-Elcrat type and quadratic functionals related to harmonic maps using advanced potential theory and capacity estimates.
Contribution
It introduces new estimates for singular sets of these systems employing Morrey's and Zorko's spaces, capacities, and Hausdorff measures.
Findings
Estimates of singular sets' Hausdorff dimensions
Application of Morrey and Zorko spaces to elliptic systems
Quantitative bounds on singularities for harmonic map functionals
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.