138 citations · 1.3k across the 90 of their papers we have counts for
51 papers · 1 filter
Is the optimal magnetic rectangle a square?
David Krejcirik
We are concerned with the dependence of the lowest eigenvalue of the magnetic Dirichlet Laplacian on the geometry of rectangles, subject to homogeneous fields. We conjecture that t…
Semiclassical asymptotics of the Bloch--Torrey operator in two dimensions
Frédéric Hérau, David Krejcirik, Nicolas Raymond
The Bloch--Torrey operator on a bounded smooth planar domain, subject to Dirichlet boundary conditions, is analyzed. Assuming an…
Criticality transition for positive powers of the discrete Laplacian on the half line
Borbala Gerhat, David Krejcirik, Frantisek Stampach
We study the criticality and subcriticality of powers with of the discrete Laplacian acting on . We prove that these positive powers of the…
An improved discrete Rellich inequality on the half-line
Borbala Gerhat, David Krejcirik, Frantisek Stampach
Based on a new idea of factorization, we prove an improved discrete Rellich inequality and discuss its optimality. We also give a conjecture on improved higher order discrete Hardy…
Quasi-conical domains with embedded eigenvalues
David Krejcirik, Vladimir Lotoreichik
The spectrum of the Dirichlet Laplacian on any quasi-conical open set coincides with the non-negative semi-axis. We show that there is a connected quasi-conical open set such that…
Spectrum of the wave equation with Dirac damping on a non-compact star graph
David Krejcirik, Julien Royer
We consider the wave equation on non-compact star graphs, subject to a distributional damping defined through a Robin-type vertex condition with complex coupling. It is shown that…