Abstract In this paper, we consider the first Steklov–Dirichlet eigenvalue of Laplace operator in annular domains with a spherical hole. We prove monotonicity result respect to hole, when outer region is centrally symmetric.

In this study, some estimations of convolution type operators defined with the help Steklov operator in weighted Lorentz space L_ω^(p,q) (T) are obtained. Also, basic properties these spaces investigated.

Abstract Recently, D. Bucur and M. Nahon used boundary homogenisation to show the remarkable flexibility of Steklov eigenvalues planar domains. In present paper we extend their result higher dimensions arbitrary manifolds with boundary, even though in those cases does not generally exhibit any periodic structure. Our arguments use a framework variational provide different proof original results...

In this article we study the nonlinear Steklov boundary-value problem ∆p(x)u = |u|p(x)−2u in Ω, |∇u|p(x)−2 ∂u ∂ν = λf(x, u) on ∂Ω. Using the variational method, under appropriate assumptions on f , we obtain results on existence and multiplicity of solutions.

In this paper we study the first Steklov-Laplacian eigenvalue with an internal fixed spherical obstacle. We prove that shell locally maximizes among nearly sets when both ball and volume are fixed.

We consider a shape optimization problem for the first mixed Steklov–Dirichlet eigenvalues of domains bounded by two balls in two-point homogeneous space. give geometric proof which is motivated Newton’s shell theorem.

This paper discusses efficient numerical methods for the Steklov eigenvalue problem and establishes a new multiscale discretization scheme and an adaptive algorithm based on the Rayleigh quotient iterative method. The efficiency of these schemes is analyzed theoretically, and the constants appeared in the error estimates are also analyzed elaborately. Finally, numerical experiments are provided...

We study the existence of eigenvalues for a two parameter Steklov eigenvalues problem with weights. Moreover, we prove the simplicity and the isolation results of the principal eigenvalue. Finally, we obtain the continuity and the differentiability of this principal eigenvalue. AMS Subject Classifications: 35J60, 35B33.

In hep-th/0202087 it was argued that the operator L0 is bad defined in κ-basis as a kernel operator. Indeed, we show that L0 is a difference operator. We also find a representation of L1 and L−1 in a class of difference operators. On leave from Steklov Mathematical Institute, Moscow, Russia.