79 citations · 481 across the 62 of their papers we have counts for
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A geometric bound on the lowest magnetic Neumann eigenvalue via the torsion function
Ayman Kachmar, Vladimir Lotoreichik
We obtain an upper bound on the lowest magnetic Neumann eigenvalue of a bounded, convex, smooth, planar domain with moderate intensity of the homogeneous magnetic field. This bound…
Isoperimetric inequalities for inner parallel curves
Charlotte Dietze, Ayman Kachmar, Vladimir Lotoreichik
We prove weighted isoperimetric inequalities for smooth, bounded, and simply connected domains. More precisely, we show that the moment of inertia of inner parallel curves for doma…
Optimisation and monotonicity of the second Robin eigenvalue on a planar exterior domain
David Krejcirik, Vladimir Lotoreichik
We consider the Laplace operator in the exterior of a compact set in the plane, subject to Robin boundary conditions. If the boundary coupling is sufficiently negative, there are a…
Spectral asymptotics of the Dirac operator in a thin shell
Vladimir Lotoreichik, Thomas Ourmières-Bonafos
We investigate the spectrum of the Dirac operator with infinite mass boundary conditions posed in a tubular neighborhood of a smooth compact hypersurface in without…
Spectral analysis of the Dirac operator with a singular interaction on a broken line
Dale Frymark, Markus Holzmann, Vladimir Lotoreichik
We consider the one-parametric family of self-adjoint realizations of the two-dimensional massive Dirac operator with a Lorentz scalar -shell interaction of strength $τ\in\mathb…
Improved inequalities between Dirichlet and Neumann eigenvalues of the biharmonic operator
Vladimir Lotoreichik
We prove that the -th Neumann eigenvalue of the biharmonic operator on a bounded connected -dimensional Lipschitz domain is not larger than its -th Dirichlet…