arXiv subjects

Nausica Aldeghi

Publications and source records attributed to Nausica Aldeghi.

3 recordsLinked to original sources

arXiv2025

On the first eigenvalue and eigenfunction of the Laplacian with mixed boundary conditions

We consider the eigenvalue problem for the Laplacian with mixed Dirichlet and Neumann boundary conditions. For a certain class of bounded, simply connected planar domains we prove monotonicity properties of the first eigenfunction. As a consequence, we establish a variant of the hot spots conjecture for mixed boundary conditions. Moreover, we obtain an inequality between the lowest eigenvalue of this mixed problem and the lowest eigenvalue of the corresponding dual problem where the Dirichlet and Neumann boundary conditions are interchanged. The proofs are based on a novel variational principle, which we establish.

math.SP↗

arXiv2024

Inequalities for eigenvalues of Schrödinger operators with mixed boundary conditions

We consider the eigenvalue problem for the Schrödinger operator on bounded, convex domains with mixed boundary conditions, where a Dirichlet boundary condition is imposed on a part of the boundary and a Neumann boundary condition on its complement. We prove inequalities between the lowest eigenvalues corresponding to two different choices of such boundary conditions on both planar and higher-dimensional domains. We also prove an inequality between higher order mixed eigenvalues and pure Dirichlet eigenvalues on multidimensional polyhedral domains.

math.SP↗

arXiv2023

Inequalities between the lowest eigenvalues of Laplacians with mixed boundary conditions

The eigenvalue problem for the Laplacian on bounded, planar, convex domains with mixed boundary conditions is considered, where a Dirichlet boundary condition is imposed on a part of the boundary and a Neumann boundary condition on its complement. Given two different such choices of boundary conditions for the same domain, we prove inequalities between their lowest eigenvalues. As a special case, we prove parts of a conjecture on the order of mixed eigenvalues of triangles.

math.SP↗