6 papers
A Product Principle for Harmonic Schwarz Lemmas: Boxes, Polydiscs, and Metric Geometry
Miljan Knežević, Miodrag Mateljević
We establish an exact product principle for the Euclidean operator norm of differentials of harmonic maps. For a bounded domain \(G\subset\R^m\) and \(p\in G\), let \(M_G(p)\) deno…
Target Geometry in Prescribed-Value Schwarz Lemmas for Harmonic Maps
Miljan Knežević, Miodrag Mateljević
We study harmonic maps \(F:\D\to G\) into bounded domains in real Hilbert spaces, prescribing \(F(0)\) and \(dF_0(\R^2)\) when \(dF_0\) is nonzero and conformal. We prove a target-…
On Montel theorem for mappings with inverse moduli inequalities
Miodrag Mateljevic, Evgeny Sevost'yanov
This paper is devoted to the study of mappings with finite distortion, in particular, mappings satisfying the inverse Poletskii inequality. We study the problem of equicontinuity o…
On Lipschitz continuity and smoothness up to the boundary of solutions of hyperbolic Poisson's equation
Miodrag Mateljević, Nikola Mutavdžić
We solve the Dirichlet problem for hyperbolic Poisson's equation where and is a measure that sati…
Hölder and Lipschitz continuity in Orlicz-Sobolev classes, distortion and harmonic mappings
Miodrag Mateljević, Ruslan Salimov, Evgeny Sevost'Yanov
In this article, we consider the Hölder continuity of injective maps in Orlicz-Sobolev classes defined on the unit ball. Under certain conditions on the growth of dilatations, we o…
Schwarz-Pick Lemma for Harmonic and Hyperbolic Harmonic Functions
Adel Khalfallah, Bojana Purtić, Miodrag Mateljević
We establish some inequalities of Schwarz-Pick type for harmonic and hyperbolic harmonic functions on the unit ball of and we disprove a recent conjecture of Liu [Schwarz-Pick Lemm…