Sharp polynomial bounds on the number of scattering poles for metric perturbations of the Laplacian in IRn.
Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the laplacian on thin planar domains
Singular non polynomial perturbations of
Si studia la perturbazione dello spettro deiroperatore dovuta all'introduzione di un potenziale singolare non polinomiale e si prova che la serie perturbativa del primo autovalore di tale operatore è sommabile secondo Borel.
Singular perturbations and parameter-dependent pseudo-differential boundary problems
Singular Solutions of the p-Laplace Equation (Erratum).
Singularités des problèmes aux limites dans des polyèdres
Singularities in two- and three-dimensional elliptic problems and finite element methods for their treatment
Sojourn times of trapping rays and the behavior of the modified resolvent of the laplacian
Solution of the Dirichlet problem for the Laplace equation
For open sets with a piecewise smooth boundary it is shown that a solution of the Dirichlet problem for the Laplace equation can be expressed in the form of the sum of the single layer potential and the double layer potential with the same density, where this density is given by a concrete series.
Solution of the Dirichlet problem with l^p boundary condition
Solution of the first biharmonic problem by the method of least squares on the boundary
Solution of the Neumann problem for the Laplace equation
For fairly general open sets it is shown that we can express a solution of the Neumann problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series. If the open set is simply connected and bounded then the solution of the Dirichlet problem is the double layer potential with a density given by a similar series.
Solution of the Robin problem for the Laplace equation
For open sets with a piecewise smooth boundary it is shown that we can express a solution of the Robin problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series.
Solvability of the Poisson equation in weighted Sobolev spaces
The aim of this paper is to prove the existence of solutions to the Poisson equation in weighted Sobolev spaces, where the weight is the distance to some distinguished axis, raised to a negative power. Therefore we are looking for solutions which vanish sufficiently fast near the axis. Such a result is useful in the proof of the existence of global regular solutions to the Navier-Stokes equations which are close to axially symmetric solutions.
Solving heat and wave-like equations using He's polynomials.
Solving the Dirichlet acoustic scattering problem for a surface with added bumps using the Green's function for the original surface.
Some asymptotic formulae for spectra of a general convex domain.
Some Current Questions on Solving Linear Elliptic Problems.
Some geometric properties for a class of non-Lipschitz domains.
Some mixed finite element methods on anisotropic meshes
The paper deals with some mixed finite element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived in some anisotropic weighted Sobolev spaces. As particular applications, the numerical approximation by mixed methods of the Laplace equation in domains with edges is investigated where anisotropic finite element meshes are appropriate. Optimal error estimates are obtained using some anisotropic...