Jonathan Rohleder

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20142024

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math.SP2024

A variational approach to the hot spots conjecture

Jonathan Rohleder

We review a recent new approach to the study of critical points of Laplacian eigenfunctions. Its core novelty is a non-standard variational principle for the eigenvalues of the Lap…

math.SP2023

Inequalities between the lowest eigenvalues of Laplacians with mixed boundary conditions

Nausica Aldeghi, Jonathan Rohleder

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…

math.SP2014

An eigenvalue inequality for Schrödinger operators with $δ$ and $δ^{'}$ -interactions supported on hypersurfaces

Vladimir Lotoreichik, Jonathan Rohleder

We consider self-adjoint Schrödinger operators in $L^{2} (R^{d})$ with a $δ$ -interaction of strength $α$ and a $δ^{'}$ -interaction of strength $β$ , respectively, supported on a h…

A variational approach to the hot spots conjecture

Inequalities between the lowest eigenvalues of Laplacians with mixed boundary conditions

An eigenvalue inequality for Schrödinger operators with δ and δ′-interactions supported on hypersurfaces

An eigenvalue inequality for Schrödinger operators with $δ$ and $δ^{'}$ -interactions supported on hypersurfaces