138 citations · 1.3k across the 90 of their papers we have counts for
12 papers · 1 filter
Optimisation of the lowest Robin eigenvalue in exterior domains of the hyperbolic plane
Antonio Celentano, David Krejcirik, Vladimir Lotoreichik
We consider the Robin Laplacian in the exterior of a bounded simply-connected Lipschitz domain in the hyperbolic plane. We show that the essential spectrum of this operator is $[\f…
Uniform resolvent estimates and absence of eigenvalues of biharmonic operators with complex potentials
Lucrezia Cossetti, Luca Fanelli, David Krejcirik
We quantify the subcriticality of the bilaplacian in dimensions greater than four by providing explicit repulsivity/smallness conditions on complex additive perturbations under whi…
Hardy inequalities for magnetic -Laplacians
Cristian Cazacu, David Krejcirik, Nguyen Lam +1
We establish improved Hardy inequalities for the magnetic -Laplacian due to adding nontrivial magnetic fields. We also prove that for Aharonov-Bohm magnetic fields the sharp con…
Location of hot spots in thin curved strips
David Krejcirik, Matěj Tušek
The maxima and minima of Neumann eigenfunctions of thin tubular neighbourhoods of curves on surfaces are located in terms of the maxima and minima of Neumann eigenfunctions of the…
The equality case in a Poincaré-Wirtinger type inequality
B. Brandolini, F. Chiacchio, D. Krejčiřík +1
In this paper, generalizing to the non smooth case already existing results, we prove that, for any convex planar set , the first non-trivial Neumann eigenvalue of the…
Nodal sets of thin curved layers
David Krejcirik, Matej Tusek
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 arbit…
The Brownian traveller on manifolds
Martin Kolb, David Krejcirik
We study the influence of the intrinsic curvature on the large time behaviour of the heat equation in a tubular neighbourhood of an unbounded geodesic in a two-dimensional Riemanni…
The improved decay rate for the heat semigroup with local magnetic field in the plane
David Krejcirik
We consider the heat equation in the presence of compactly supported magnetic field in the plane. We show that the magnetic field leads to an improvement of the decay rate of the h…
The asymptotic behaviour of the heat equation in a twisted Dirichlet-Neumann waveguide
David Krejcirik, Enrique Zuazua
We consider the heat equation in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary condition…
On some strong ratio limit theorems for heat kernels
M. Fraas, D. Krejcirik, Y. Pinchover
We study strong ratio limit properties of the quotients of the heat kernels of subcritical and critical operators which are defined on a noncompact Riemannian manifold.
The Hardy inequality and the heat equation in twisted tubes
David Krejcirik, Enrique Zuazua
We show that a twist of a three-dimensional tube of uniform cross-section yields an improved decay rate for the heat semigroup associated with the Dirichlet Laplacian in the tube.…
Instability results for the damped wave equation in unbounded domains
Pedro Freitas, David Krejcirik
We extend some previous results for the damped wave equation in bounded domains in Euclidean spaces to the unbounded case. In particular, we show that if the damping term is of the…