SMS scnews item created by Daniel Hauer at Mon 24 Jul 2023 1003
Type: Seminar
Modified: Mon 24 Jul 2023 1101
Distribution: World
Expiry: 26 Jul 2023
Calendar1: 26 Jul 2023 1200-1300
CalLoc1: AGR Carslaw 829
CalTitle1: Eigenvalue problems on disconnected domains
Auth: dhauer@p613m3.pc (assumed)

Informal working seminar on Analysis and PDEs

Eigenvalue problems on disconnected domains

Zeaiter Zeaiter

Dear friends and colleagues,

in this informal working seminar on topics in Analysis and PDE
our colleague Zeaiter is providing us with a glimpse into his research interest.

He is speaking about

Eigenvalue problems on disconnected domains


In this presentation, we will investigate elliptic eigenvalue problems on disconnected
domains. Of particular interest will be the case, where we consider an eigenvalue problem
with a parameterized potential

        \( -\Delta u_{\lambda} + \lambda\, m\, u_{\lambda} = \mu(\lambda)\, u_{\lambda}. \)

Here, \(m\in L^{\infty}\) with a disconnected zero set.

We will investigate, in some simple cases the limit as \(\lambda\to\infty\) and show that there is
an eigenpair \((u_{\infty},\lambda_{\infty})\) which is the limit of the sequence of eigenpairs \((u_{\lambda},\mu(\lambda))\) as
\(\lambda\to\infty\), and the pair \((u_{\infty},\lambda_{\infty})\) is a solution of the equation

        \( -\Delta u_{\infty} = \mu(\infty)\, u_{\infty}. \)

Everyone interested in Analysis and PDEs is warmly invited to attend this seminar.

Best wishes,