Shape derivative of the first eigenvalue of the 1-Laplacian
Nicolas Saintier
TL;DR
This paper computes the shape derivative of the first eigenvalue of the 1-Laplacian and shows that a ball is a critical shape under volume-preserving deformations.
Contribution
It provides the first calculation of the shape derivative for the 1-Laplacian's first eigenvalue and characterizes critical shapes.
Findings
A ball is critical among all volume-preserving deformations.
The shape derivative of the first eigenvalue is explicitly computed.
Abstract
We compute the shape derivative of the first eigenvalue of the 1-Laplacian. As an application, we find that a ball is critical among all volume-preserving deformations.
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 Mathematical Modeling in Engineering · Spectral Theory in Mathematical Physics · Nonlinear Partial Differential Equations