Properties of Solutions of Differential Equations on Foliations
Xiaoai Chai, John Eric Fornaess
TL;DR
This paper studies differential equations on foliations by real curves, focusing on the existence of a continuous solution operator when the input function is continuous.
Contribution
It introduces a framework for differential equations on foliations ensuring solutions depend continuously on the data.
Findings
Established conditions for continuous solution operators
Analyzed properties of differential equations on foliations
Provided insights into the structure of solutions
Abstract
In this paper, we discuss foliations by real curves. We investigate differential equations which are modifications of du/dx = v along leaves. Our focus is on having a solution operator so that u is continuous if v is continuous.
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.
Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Meromorphic and Entire Functions · Differential Equations and Numerical Methods