Michael Poghosyan

Yerevan State University | YSU · Faculty of Mathematics and Mechanics

We generalize an important property of trigonometric series to the case of series by orthonormal spline systems corresponding to the dyadic sequence of grid points. We prove that Ciesielski series cannot diverge to infinity on a set of positive measure.

In this paper, we obtain recovery formulas for coefficients of multiple Franklin series by means of its sum, if the series satisfies the following conditions: 1) the square partial sums with indices 2ν converge almost everywhere, 2) the majorant of partial sums with indices 2ν satisfies some necessary condition.

We propose an algorithm to solve the two-phase obstacle problem by finite difference method. We prove the existence and uniqueness of the solution of the discrete nonlinear system and obtain an error estimate for the corresponding regularization. Also we prove the convergence of the proposed numerical algorithm. At the end of the paper we present s...

In this paper we consider the numerical approximation of the two-phase membrane (obstacle) problem by finite difference method. First, we introduce the notion of viscosity solution for the problem and construct certain discrete nonlinear approximation system. The existence and uniqueness of the solution of the discrete nonlinear system is proved. B...

In this paper we consider the finite difference scheme approximation for one-phase obstacle problem and obtain an error estimate for this approximation. KeywordsFree boundary problem–obstacle problem–finite difference method

We propose an algorithm to solve the \textit{two-phase obstacle problem} by finite difference method. We obtain an error estimate for finite difference approximation and prove the convergence of proposed algorithm.

We study optimal 2-switching and nn-switching problems and the corresponding system of variational inequalities. We obtain results on the existence of viscosity solutions for the 2-switching problem for various setups when the cost of switching is non-deterministic. For the nn-switching problem we obtain regularity results for the solutions of the...

This paper studies a free boundary problem for the heat equation in a convex ring. It is proved that the considered problem has unique solution under some conditions on the initial data.

For a given convex ring and an L 1 function f:Ω × → + we show, under suitable assumptions on f, that there exists a solution (in the weak sense) to with {x Ω: u(x) > s} Ω1 convex, for all s (0, M).

The main result of this paper concerns existence of classical solutions to the multi-layer Bernoulli free boundary problem with nonlinear joining conditions and the p-Laplacian as gov-erning operator. The present treatment of the 2-layer case involves technical refinements of the one-layer case, studied earlier by two of the authors. The existence...

A criterion for almost everywhere convergence of series with respect to generalized Franklin systems is derived extending a result for classical Franklin system proved by G. G. Gevorkian [Anal. Math. 16, No. 2, 87-114 (1990; Zbl 0706.42019)].

The paper investigates uniqueness of almost everywhere convergent series with respect to a generalized Franklin system.