On the optimal growth of functions with bounded Laplacian.
On the order of starlikeness and convexity of complex harmonic functions with a two-parameter coefficient condition
The article of J. Clunie and T. Sheil-Small [3], published in 1984, intensified the investigations of complex functions harmonic in the unit disc Δ. In particular, many papers about some classes of complex mappings with the coefficient conditions have been published. Consideration of this type was undertaken in the period 1998-2004 by Y. Avci and E. Złotkiewicz [2], A. Ganczar [5], Z. J. Jakubowski, G. Adamczyk, A. Łazińska and A. Sibelska [1], [8], [7], H. Silverman [12] and J. M. Jahangiri [6],...
On the orthogonal projections onto spaces of pluriharmonic functions and duality
On the -boundedness of nonisotropic spherical Riesz potentials.
On the parabolic potentials in degenerate-type heat equation.
On the Poisson equation in the potential theory of a single kernel.
On the Poisson integral for Lipschitz and -domains
On the potential theory of some systems of coupled PDEs
In this paper we study some potential theoretical properties of solutions and super-solutions of some PDE systems (S) of type , , on a domain of , where and are suitable measures on , and , are two second order linear differential elliptic operators on with coefficients of class . We also obtain the integral representation of the nonnegative solutions and supersolutions of the system (S) by means of the Green kernels and Martin boundaries associated with and , and a convergence...
On the radial boundary values of subharmonic functions.
On the rank of harmonic maps.
On the reduced modulus of a half-strip.
On the Regularity of Alexandrov Surfaces with Curvature Bounded Below
In this note, we prove that on a surface with Alexandrov’s curvature bounded below, the distance derives from a Riemannian metric whose components, for any p ∈ [1, 2), locally belong to W1,p out of a discrete singular set. This result is based on Reshetnyak’s work on the more general class of surfaces with bounded integral curvature.
On the Regularity of the Solution of the Biharmonic Variational Inequality.
On the relation between elliptic and parabolic Harnack inequalities
We show that, if a certain Sobolev inequality holds, then a scale-invariant elliptic Harnack inequality suffices to imply its a priori stronger parabolic counterpart. Neither the relative Sobolev inequality nor the elliptic Harnack inequality alone suffices to imply the parabolic Harnack inequality in question; both are necessary conditions. As an application, we show the equivalence between parabolic Harnack inequality for on , (i.e., for ) and elliptic Harnack inequality for on .
On the representation of Dirichlet forms
A general representation theorem is obtained for positive quadratic forms, defined on (the space of continuously differentiable functions with compact support contained in ) which are local and on which all normal contractions operate.
On the reproducing kernel for harmonic functions and the space of Bloch harmonic functions on the unit ball in
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...
On the sense preserving mappings in the Helm topology in the plane
∗Research supported by the grant No. GAUK 186/96 of Charles University.We introduce the helm topology in the plane. We show that (assuming the helm local injectivity and the Euclidean continuity) each mapping which is oriented at all points of a helm domain U is oriented at U.
On the sharpness of the Stolz approach.
On the Skew Product of Symmetric Diffusion Processes.