This paper deals with the fractional Sobolev spaces Ws, p. We analyze the relations among
some of their possible definitions and their role in the trace theory. We prove continuous and …

arXiv:0901.3261v1 [math.PR] 21 Jan 2009 Page 1 arXiv:0901.3261v1 [math.PR] 21 Jan 2009
FROM THE LONG JUMP RANDOM WALK TO THE FRACTIONAL LAPLACIAN ENRICO …

This paper proposes the singular boundary method (SBM) in conjunction with Burton and
Miller׳ s formulation for acoustic radiation and scattering. The SBM is a strong-form …

It is well known that the standard finite element method (FEM) is unreliable to solve acoustic
problems governed by the Helmholtz equation with large wave numbers due to the “overly …

A domain decomposition method is presented for analyzing electromagnetic problems
involving multiple separable scatterers. The method first decomposes the original problem …

We study the concentration phenomenon for solutions of the fractional nonlinear Schr\"{o}
dinger equation, which is nonlocal. We mainly use the Lyapunov-Schmidt reduction method …

In this paper, the stable node-based smoothed finite element method (SNS-FEM) and the
well-known Dirichlet-to-Neumann (DtN) boundary condition are coupled together to reduce …

Consider the scattering of a time-harmonic acoustic incident wave by a bounded, penetrable
and isotropic elastic solid, which is immersed in a homogeneous compressible air/fluid. By …

An improved interpolating element-free Galerkin (IIEFG) method coupled with Modified
Dirichlet-to-Neumann (MDtN) boundary condition is presented in this paper for use in …

This paper proposes the boundary element-free method (BEFM) for the numerical solution of
exterior acoustic problems with arbitrary and high wavenumbers. A single layer BEFM and a …