**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**

**Abstract**

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,

Daniel