Internal and external one-sided homogeneous boundary value problems of conjugation for bicircular domains of the space .
Jump conditions for a metaharmonic double layer potential on rectifiable closed Jordan curves in ℝ²
This paper is concerned with jump conditions for the double layer potential associated with the two-dimensional Helmholtz equation for Hölder continuous boundary data on arbitrary rectifiable Jordan closed curves in ℝ².
Laplace transform representations and Paley-Wiener theorems for functions on vertical strips.
Layer potentials C*-algebras of domains with conical points
To a domain with conical points Ω, we associate a natural C*-algebra that is motivated by the study of boundary value problems on Ω, especially using the method of layer potentials. In two dimensions, we allow Ω to be a domain with ramified cracks. We construct an explicit groupoid associated to ∂Ω and use the theory of pseudodifferential operators on groupoids and its representations to obtain our layer potentials C*-algebra. We study its structure, compute the associated K-groups, and prove Fredholm...
Method of interior boundaries in a mixed problem of acoustic scattering.
Multiple layer potentials for the quadrant and their application to the Dirichlet problem in plane domains with a piecewise smooth boundary
New generalizations of the Poisson kernel.
Nonlinear Leray-Schauder alternatives and application to nonlinear problem arising in the theory of growing cell population
Motivated by a mathematical model of an age structured proliferating cell population, we state some new variants of Leray-Schauder type fixed point theorems for (ws)-compact operators. Further, we apply our results to establish some new existence and locality principles for nonlinear boundary value problem arising in the theory of growing cell population in L 1-setting. Besides, a topological structure of the set of solutions is provided.
O zonální funkci harmonické
On a generalized logarithmic kernel and its potentials
On a heat potential (Preliminary communication)
On generalized Fatou theorems for the square root of the Poisson kernel and in rank one symmetric space
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 solution of the integral equations for the potential problems of two circular-strips.
On the boundness of the Stokes semigroup in two-dimensional exterior domains.
On the convergence of Neumann series for noncompact operators
On the integral representation of superbiharmonic functions
We consider a nonnegative superbiharmonic function satisfying some growth condition near the boundary of the unit disk in the complex plane. We shall find an integral representation formula for in terms of the biharmonic Green function and a multiple of the Poisson kernel. This generalizes a Riesz-type formula already found by the author for superbihamonic functions satisfying the condition in the unit disk. As an application we shall see that the polynomials are dense in weighted Bergman...
On the parabolic potentials in degenerate-type heat equation.
Potential type operators on curves with vorticity points.
Quadrature of singular integrands over surfaces.