Abstract We show that Steklov eigenfunctions in a bounded Lipschitz domain have wavelength dense nodal sets near the boundary, contrast to what can happen deep inside domain. Conversely, 2D $\Omega $, we prove any of eigenfunction contains half-ball centered at $\partial \Omega $ radius $c_{\Omega }/{\lambda }$.

Bell’s theorem states that some quantum correlations can not be represented by classical correlations of separated random variables. It has been interpreted as incompatibility of the requirement of locality with quantum mechanics. We point out that in fact the space part of the wave function was neglected in the proof of Bell’s theorem. However this space part is crucial for considerations of p...

Here Ω is a bounded domain in RN with smooth boundary, ∆pu = div(|∇u|p−2∇u) is the p-Laplacian, and ∂/∂ν is the outer normal derivative. In the linear case, that is for p = 2, this eigenvalue problem is known as the Steklov problem (see [3]). Problems of the form (1.1) appear in a natural way when one considers the Sobolev trace inequality. In fact, the immersionW1,p(Ω) ↪→ Lp(∂Ω) is compact, he...

We use the string hypothesis for the mirror theory to derive the Thermodynamic Bethe Ansatz equations for the AdS5 × S mirror model. We further demonstrate how these equations can be used to construct the associated Y-system recently discussed in the literature, putting particular emphasis on the assumptions and the range of validity of the corresponding construction. Email: [email protected]...

Galerkin boundary element methods for the solution of novel first kind Steklov–Poincaré and hypersingular operator boundary integral equations with nonlinear perturbations are investigated to solve potential type problems in twoand three-dimensional Lipschitz domains with nonlinear boundary conditions. For the numerical solution of the resulting Newton iterate linear boundary integral equations...

A.V. Duplinskiy, 2 E.O. Kiktenko, 3 N.O. Pozhar, M.N. Anufriev, R.P. Ermakov, A.I. Kotov, A.V. Brodsky, R.R. Yunusov, V.L. Kurochkin, A.K. Fedorov, 6, ∗ and Y.V. Kurochkin Russian Quantum Center, Skolkovo, Moscow 143025, Russia Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 141700, Russia Steklov Mathematical Institute of Russian Academy of Sciences, Moscow 119991, Russi...