Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Research & business

Research lectures, seminars and events

The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but  wish to enquire about attending one of the events please contact the organiser or host department.


 

Analysis and/of PDE: Courant-sharp Robin eigenvalues for the square

Presented by Katie Gittins, Neuchatel (soon Durham)
17 June 2020 11:00 in zoom

Let $\Omega$ be a planar, bounded, connected, open set with Lipschitz boundary. Let $u$ be an eigenfunction of the Laplacian on $\Omega$ with either a Dirichlet, Neumann or Robin boundary condition. We are interested in the number of nodal domains of $u$.

If an eigenfunction $u$ associated with the $k$--th eigenvalue has exactly $k$ nodal domains, then we call it a Courant-sharp eigenfunction. In this case, we call the corresponding eigenvalue Courant-sharp.

The Courant-sharp Dirichlet, respectively Neumann, eigenvalues of the square are known due to Pleijel, B\'erard--Helffer, respectively Helffer--Persson-Sundqvist.

We discuss whether the Robin eigenvalues of the square are Courant-sharp.

This is based on joint work with B. Helffer (Universit\'e de Nantes).

Contact megan.k.griffin-pickering@durham.ac.uk for more information