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Displaying 1001 – 1020 of 1782

On the order of starlikeness and convexity of complex harmonic functions with a two-parameter coefficient condition

Agnieszka Sibelska (2010)

Annales UMCS, Mathematica

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

Ewa Ligocka (1986)

Studia Mathematica

On the $(p, q)$ -boundedness of nonisotropic spherical Riesz potentials.

Sarikaya, Mehmet Zeki, Yildirim, Hüseyin (2007)

Journal of Inequalities and Applications [electronic only]

On the parabolic potentials in degenerate-type heat equation.

Malyshev, Igor (1991)

Journal of Applied Mathematics and Stochastic Analysis

On the Poisson equation in the potential theory of a single kernel.

E. Nummelin (1991)

Mathematica Scandinavica

On the Poisson integral for Lipschitz and $C^{1}$ -domains

Björn Dahlbert (1979)

Studia Mathematica

On the potential theory of some systems of coupled PDEs

Abderrahim Aslimani, Imad El Ghazi, Mohamed El Kadiri, Sabah Haddad (2016)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study some potential theoretical properties of solutions and super-solutions of some PDE systems (S) of type $L_{1} u = - μ_{1} v$ , $L_{2} v = - μ_{2} u$ , on a domain $D$ of $ℝ^{d}$ , where $μ_{1}$ and $μ_{2}$ are suitable measures on $D$ , and $L_{1}$ , $L_{2}$ are two second order linear differential elliptic operators on $D$ with coefficients of class $𝒞^{\infty}$ . 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 $L_{1}$ and $L_{2}$ , and a convergence...

On the radial boundary values of subharmonic functions.

Björn E.J. Dahlberg (1977)

Mathematica Scandinavica

On the rank of harmonic maps.

Jerry L. Kazdan, Zhiren Jin (1991)

Mathematische Zeitschrift

On the reduced modulus of a half-strip.

Emel'yanov, E.G. (2004)

Zapiski Nauchnykh Seminarov POMI

On the Regularity of Alexandrov Surfaces with Curvature Bounded Below

Luigi Ambrosio, Jérôme Bertrand (2016)

Analysis and Geometry in Metric Spaces

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.

Jens Frehse (1973)

Manuscripta mathematica

On the relation between elliptic and parabolic Harnack inequalities

Waldemar Hebisch, Laurent Saloff-Coste (2001)

Annales de l’institut Fourier

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 $Δ$ on $M$ , (i.e., for $\partial_{t} + Δ$ ) and elliptic Harnack inequality for $- \partial_{t}^{2} + Δ$ on $ℝ \times M$ .

On the representation of Dirichlet forms

Lars-Erik Andersson (1975)

Annales de l'institut Fourier

A general representation theorem is obtained for positive quadratic forms, defined on $C_{00}^{1} (Ω)$ (the space of continuously differentiable functions with compact support contained in $Ω \subset R^{n}$ ) 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 $R^{n}$

Ewa Ligocka (1987)

Studia Mathematica

On the Riemann-Hilbert problem in multiply connected domains

Vladimir Ryazanov (2016)

Open Mathematics

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

Pyrih, Pavel (1999)

Serdica Mathematical Journal

∗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.

Currently displaying 1001 – 1020 of 1782

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Displaying 1001 – 1020 of 1782

On the order of starlikeness and convexity of complex harmonic functions with a two-parameter coefficient condition

On the orthogonal projections onto spaces of pluriharmonic functions and duality

On the $(p, q)$ -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 $C^{1}$ -domains

On the potential theory of some systems of coupled PDEs

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

On the Regularity of the Solution of the Biharmonic Variational Inequality.

On the relation between elliptic and parabolic Harnack inequalities

On the representation of Dirichlet forms

On the reproducing kernel for harmonic functions and the space of Bloch harmonic functions on the unit ball in $R^{n}$

On the Riemann-Hilbert problem in multiply connected domains

On the sense preserving mappings in the Helm topology in the plane

On the sharpness of the Stolz approach.

On the Skew Product of Symmetric Diffusion Processes.

On the space and dual space of functions representable by differences of subharmonic functions

Currently displaying 1001 – 1020 of 1782