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 $c_{\Omega }/{\lambda }$.

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...

In this paper we study interface equations associated to the Darcy-Stokes problem 8 using the classical Steklov-Poincaré approach and a new one called augmented. We compare 9 these two families of methods and characterize at the discrete level suitable preconditioners 10 with additive and multiplicative structures. Finally, we present some numerical results to as11 sess their behavior in presen...

We prove some results about the first Steklov eigenvalue d1 of the biharmonic operator in bounded domains. Firstly, we show that Fichera’s principle of duality [9] may be extended to a wide class of nonsmooth domains. Next, we study the optimization of d1 for varying domains: we disprove a long-standing conjecture, we show some new and unexpected features and we suggest some challenging problem...