| Description: | [DMS Seminar] Dr Anisa Chorwadwala (IISER Pune) -- An eigenvalue optimization problem over a family of planar punctured disks where the puncture has a dihedral symmetry |
| Date: | Monday, Dec 12, 2016 |
| Time: | 3 p.m. - 4 p.m. |
| Venue: | G09, Lecture Hall Complex |
| Details: | We deal with the following eigenvalue optimization problem: Given a bounded open disk $B$ in a plane, how to place an obstacle $P$ of fixed shape and size within $B$ so as to maximize or minimize the fundamental eigenvalue $\lambda_1$ of the Dirichlet Laplacian on $B \setmunus P$. This means that we want to extremize the function $\rho \rightarrow \lambda_1(B \setminus \rho(P))$, where $\rho$ runs over the set of rigid motions such that $\rho(P) \subset B$. We answer this problem in the case where $P$ is invariant under the action of a dihedral group $D_{2n}$, and where the distance from the center of the obstacle $P$ to the boundary is monotonous as a function of the argument between two axes of symmetry. The extremal configurations correspond to the cases where the axes of symmetry of $P$ coincide with a diameter of $B$. The maximizing and the minimizing configurations are identified. |
| Calendar: | Seminar Calendar (entered by saugata.bandyopadhyay) |