On an optimal decomposition in Zygmund spaces.
On approximation of the Neumann problem by the penalty method
We prove that penalization of constraints occuring in the linear elliptic Neumann problem yields directly the exact solution for an arbitrary set of penalty parameters. In this case there is a continuum of Lagrange's multipliers. The proposed penalty method is applied to calculate the magnetic field in the window of a transformer.
On certain reflexion principes
On Conjugate Gradient Type Methods and Polynomial Preconditioners for a Class of Complex Non-Hermitian Matrices.
On determining a riemannian manifold from the Dirichlet-to-Neumann map
On FE-grid relocation in solving unilateral boundary value problems by FEM
We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions. Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the...
On Finite Element Approximation of the Gradient for Solution of Poisson Equation.
On harmonic continuation of differentiable functions defined on a part of the boundary.
On Higher Riesz Transforms for Gaussian Measures.
On homogeneizatìon problems for the Laplace operator in partially perforated domains with Neumann's condition on the boundary of cavities.
In this paper the problem of homogeneization for the Laplace operator in partially perforated domains with small cavities and the Neumann boundary conditions on the boundary of cavities is studied. The corresponding spectral problem is also considered.
On mean value properties involving a logarithm-type weight
Two new assertions characterizing analytically disks in the Euclidean plane are proved. Weighted mean value property of positive solutions to the Helmholtz and modified Helmholtz equations are used for this purpose; the weight has a logarithmic singularity. The obtained results are compared with those without weight that were found earlier.
On Mixed Finite Element Methods for First Order Elliptic Systems.
On numerical solution of the Dirichlet problem by the method of locally-canonical decomposition.
On products of non-commuting sectorial operators
On quadrature methods for the double layer potential equation over the boundary of a polyhedron.
On reducing bandwidth of matrices in the Go-Away algorithm for regular grids.
On representations of real analytic functions by monogenic functions
Using the method of normalized systems of functions, we study one representation of real analytic functions by monogenic functions (i.e., solutions of Dirac equations), which is an Almansi’s formula of infinite order. As applications of the representation, we construct solutions of the inhomogeneous Dirac and poly-Dirac equations in Clifford analysis.
On shape optimization problems involving the fractional laplacian
Our concern is the computation of optimal shapes in problems involving (−Δ)1/2. We focus on the energy J(Ω) associated to the solution uΩ of the basic Dirichlet problem ( − Δ)1/2uΩ = 1 in Ω, u = 0 in Ωc. We show that regular minimizers Ω of this energy under a volume constraint are disks. Our proof goes through the explicit computation of the shape derivative (that seems to be completely new in the fractional context), and a refined adaptation of the moving plane method.
On shooting methods for the discrete Helmholtz equation with constant coefficients.
On Some High Accuracy Difference Schemes for Solving Elliptic Equations.