Non-symmetric elliptic operators on bounded Lipschitz domains in the plane.
Non-Symmetric Translation Invariant Dirichlet Forms.
Non-tangential limits of the double layer potentials
Non-tangential limits of the logarithmic potential
Nonvariational layer potentials with respect to Hölder continuous vector fields.
Norm and pointwise topologies need not be binormal.
Norm inequalities for potential-type operators.
The purpose of this paper is to derive norm inequalities for potentials of the formTf(x) = ∫(Rn) f(y)K(x,y)dy, x ∈ Rn,when K is a Kernel which satisfies estimates like those that hold for the Green function associated with the degenerate elliptic equations studied in [3] and [4].
Normal spaces and the Lusin-Menchoff property
We study the relation between the Lusin-Menchoff property and the -“semiseparation” property of a fine topology in normal spaces. Three examples of normal topological spaces having the -“semiseparation” property without the Lusin-Menchoff property are given. A positive result is obtained in the countable compact space.
Note on contractivity of the Neumann operator
Note sur des principes duaux en théorie du potentiel
Note über analytische Functionen mehrerer Veränderlicher
Nouvelles formulations intégrales pour les problèmes de diffraction d’ondes
We present an integral equation method for solving boundary value problems of the Helmholtz equation in unbounded domains. The method relies on the factorisation of one of the Calderón projectors by an operator approximating the exterior admittance (Dirichlet to Neumann) operator of the scattering obstacle. We show how the pseudo-differential calculus allows us to construct such approximations and that this yields integral equations without internal resonances and being well-conditioned at all frequencies....
Nouvelles formulations intégrales pour les problèmes de diffraction d'ondes
We present an integral equation method for solving boundary value problems of the Helmholtz equation in unbounded domains. The method relies on the factorisation of one of the Calderón projectors by an operator approximating the exterior admittance (Dirichlet to Neumann) operator of the scattering obstacle. We show how the pseudo-differential calculus allows us to construct such approximations and that this yields integral equations without internal resonances and being well-conditioned at all...
Noyaux associés à des opérateurs de Faraut
Numerical analysis of the general biharmonic problem by the finite element method
The present paper deals with solving the general biharmonic problem by the finite element method using curved triangular finit -elements introduced by Ženíšek. The effect of numerical integration is analysed in the case of mixed boundary conditions and sufficient conditions for the uniform -ellipticity are found.
Numerical solution of inverse spectral problems for Sturm-Liouville operators with discontinuous potentials
We consider Sturm-Liouville differential operators on a finite interval with discontinuous potentials having one jump. As the main result we obtain a procedure of recovering the location of the discontinuity and the height of the jump. Using our result, we apply a generalized Rundell-Sacks algorithm of Rafler and Böckmann for a more effective reconstruction of the potential and present some numerical examples.
Numerical treatment of 3-dimensional potential problem
Assuming an incident wave to be a field source, we calculate the field potential in a neighborhood of an inhomogeneous body. This problem which has been formulated in can be reduced to a bounded domain. Namely, a boundary condition for the potential is formulated on a sphere. Then the potential satisfies a well posed boundary value problem in a ball containing the body. A numerical approximation is suggested and its convergence is analyzed.