Finding the conductors in circular networks from boundary measurements
Fourier problem with bounded Baire data
The Fourier problem on planar domains with time moving boundary is considered using integral equations. Solvability of those integral equations in the space of bounded Baire functions as well as the convergence of the corresponding Neumann series are proved.
Internal and external one-sided homogeneous boundary value problems of conjugation for bicircular domains of the space .
Invariance of the Fredholm radius of an operator in potential theory
Inverse source problem in a 3D ball from best meromorphic approximation on 2D slices.
Lp estimates of boundary integral equations for some nonlinear boundary value problems.
Non-symmetric elliptic operators on bounded Lipschitz domains in the plane.
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.
On a boundary value problem for the heat equation
On a heat potential
On harmonic continuation of differentiable functions defined on a part of the boundary.
On the Neumann operator of the arithmetical mean.
On the Riemann-Hilbert problem in multiply connected domains
We proved the existence of multivalent solutions with the infinite number of branches for the Riemann-Hilbert problem in the general settings of finitely connected domains bounded by mutually disjoint Jordan curves, measurable coefficients and measurable boundary data. The theorem is formulated in terms of harmonic measure and principal asymptotic values. It is also given the corresponding reinforced criterion for domains with rectifiable boundaries stated in terms of the natural parameter and nontangential...
Positive solutions of nonlinear elliptic equations in a half space in .
Problèmes d'écrans perforés pour l'équation de Laplace
Reflection and a mixed boundary value problem concerning analytic functions
A mixed boundary value problem on a doubly connected domain in the complex plane is investigated. The solution is given in an integral form using reflection mapping. The reflection mapping makes it possible to reduce the problem to an integral equation considered only on a part of the boundary of the domain.
Reflection and the Dirichlet problem on doubly connected regions
Reflection and the Neumann problem on doubly connected regions
Réseaux électrique planaires I.
Reseaux électriques planaires II.