Mathematics Seminar: Dr. Ashok Kumar, IIT Madras: Shape variation via the geometry of eigenfunctions
Dr. Ashok Kumar, IIT Madras
| Speaker |
Dr. Ashok Kumar, IIT Madras
|
|---|---|
| When |
Oct 12, 2022
from 04:00 PM to 05:00 PM |
| Where | via zoom |
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Abstract: In this talk, we discuss some of the geometric properties of the first eigenfunctions of the Laplace operator with mixed boundary conditions over annular domains. We consider the homogeneous Dirichlet condition on the inner boundary and the homogenous Neumann condition on the outer boundary. We study the foliated Schwarz symmetry and the monotonicity along the axial and affine-radial directions of the first eigenfunctions. Using these geometric properties and shape calculus, we prove that the first eigenvalue strictly decreases when the inner ball moves towards the outer boundary. We also discuss some related open problems.