2008, Studia Mathematica 7
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The harmonic Dirichlet problem in a planar domain with cracks
(2008)The harmonic Dirichlet problem in a planar domain with smooth cracks of an arbitrary shape is considered in case, when the solution is not continuous at the ends of the cracks. The well-posed formulation of the problem ... -
Bergman kernel functions for planar domains and conformal equivalence of domains
(2008)The Bergman kernels of multiply connected domains are related with proper holomorphic maps onto the unit disc. We study multiply connected planar domains and represent conformal equivalence of the Bell representative ... -
Optimal design of unbounded 2D composite materials with circular inclusions of different radii
(2008)Optimal design problem for 2D composite materials with different circular inclusions is studied on the base of the potential method combined with functional equation method. Exact geometric description of the optimal ... -
The transmission problem for elliptic second order equations in a conical domain
(2008)The present article is a survey of our last results. We establish best possible estimates of the weak solutions to the transmission problem near conical boundary point. We study this problem for the Laplace operator ... -
Another description of continuous solutions of a nonlinear functional inequality
(2008)The paper gives a general construction of all continuous solutions of inequality (1) ful lling one of conditions (5) or (26). This paper is a continuation of [3]. -
On functional bases of the first-order differential invariants for non-conjugate subgroups of the Poincaré group $P(1,4)$
(2008)It is established which functional bases of the first-order differential invariants of the splitting and non-splitting subgroups of the Poincaré group $P(1,4)$ are invariant under the subgroups of the extended Galilei group ... -
Gauss's definition of the gamma function
(2008)The present paper gives a historical account on extending the factorial function to complex numbers by Gauss. -
Sign-changing Lyapunov functions in linear extensions of dynamical systems
(2008)In this note we consider sets of linear extensions of dynamical systems on a torus. We examine regularity of the systems by means of a given sign-changing Lyapunov function. The main result of the paper is to give ... -
Lichawski-Matkowski-Miś theorem on locally defined operators for functions of several variables
(2008)Let $D$ be a regular closed set in the open subspace $G ⊂ ℝ^n$ and $C^m(D)$ be the space of functions $f|_D$ such that $f ∈ C^m(G)$. The representation formulas for locally defined operators mapping $C^m(D)$ into $C^0(D)$ ... -
Riemann integrability of a nowhere continuous multifunction
(2008)We present an example of the Riemann integrable multifunction which is discontinuous at each point with respect to the Hausdorff metric. The constructed multifunction is neither lower nor upper semicontinuous. -
Annales Academiae Paedagogicae Cracoviensis. 63. Studia Mathematica 7
(Wydawnictwo Naukowe Akademii Pedagogicznej, Kraków, 2008)
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