Payne conjectured in 1967 that the nodal line of the second Dirichlet eigenfunction must
touch the boundary of the domain. In their 1997 breakthrough paper, Hoffmann-Ostenhof …

In this paper, we consider the optimization problem for the first Dirichlet eigenvalue λ 1 (Ω) of
the p-Laplacian Δ p, 1< p<∞, over a family of doubly connected planar domains Ω= B∖ P‾ …

We construct a multiply connected domain in R2 for which the second eigenfunction of the
Laplacian with Robin boundary conditions has an interior nodal line. In the process, we …

This paper is concerned with the location of nodal sets of eigenfunctions of the Dirichlet
Laplacian in thin tubular neighbourhoods of hypersurfaces of the Euclidean space of …

We investigate the geometry of the nodal set of a second eigenfunction of the Dirichlet
Laplacian in a doubly connected Euclidean plane domain of the form Ω= D\B and obtain …

We investigate several aspects of the nodal geometry and topology of Laplace
eigenfunctions, with particular emphasis on the low frequency regime. This includes …

Spectral theory is an extremely rich field which has found its application in many areas of
physics and mathematics. One of the reason which makes it so attractive on the formal level …

We introduce an analogue of Payne's nodal line conjecture, which asserts that the nodal
(zero) set of any eigenfunction associated with the second eigenvalue of the Dirichlet …

We revisit two 1999 papers:[1]~\emph {M.~ Hoffmann-Ostenhof, T.~ Hoffmann-Ostenhof, and
N.~ Nadirashvili. On the multiplicity of eigenvalues of the Laplacian on surfaces. Ann. Global …

In this thesis we deal with qualitative properties of solutions of the semilinear elliptic
problem−∆ u= f (u) in Ω u= 0 on∂ Ω, where Ω⊆ R^ N, N≥ 2 is a smooth domain and f: R→ …