On extremal problems related to inverse balayage.
On Fatou-Type Theorems for Non-Radial Kernels.
On generalized Fatou theorems for the square root of the Poisson kernel and in rank one symmetric space
On harmonic conjugates with exponential mean growth
On harmonic continuation of differentiable functions defined on a part of the boundary.
On harmonic functions constructed by the Hadamard product.
On harmonic functions defined by derivative operator.
On log-subharmonicity of singular values of matrices
Let F be an analytic function from an open subset Ω of the complex plane into the algebra of n×n matrices. Denoting by the decreasing sequence of singular values of a matrix, we prove that the functions and are subharmonic on Ω for 1 ≤ k ≤ n.
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 meromorphic harmonic functions with respect to -symmetric points.
On numerical solution of a variational inequality of the 4th order by finite element method
The problem of a thin elastic plate, deflection of which is limited below by a rigid obstacle is solved. Using Ahlin's and Ari-Adini's elements on rectangles, the convergence is established and SOR method with constraints is proposed for numerical solution.
On (r, 2)-capacities for a class of elliptic pseudo differential operators.
On solution of the integral equations for the potential problems of two circular-strips.
On some subclasses of harmonic functions defined by fractional calculus.
On strong tracts of subharmonic functions of infinite lower order
The notion of a strong asymptotic tract for subharmonic functions is defined. Eremenko's value b(∞,u) for subharmonic functions is introduced and it is used to provide an exact upper estimate of the number of strong tracts of subharmonic functions of infinite lower order. It is also shown that b(∞,u) ≤ π for subharmonic functions of infinite lower order.
On the boundness of the Stokes semigroup in two-dimensional exterior domains.
On the continuity of heat potentials
On the convergence of Neumann series for noncompact operators
On the Convergence of the Conjugate Gradient Method for Singular Capacitance Matrix Equations from the Neumann Problem of the Poisson Equation.
On the dimension of -harmonic measure.