417 research outputs found
On integral conditions in the mapping theory
It is established interconnections between various integral conditions that
play an important role in the theory of space mappings and in the theory of
degenerate Beltrami equations in the plane.Comment: 15 pages, changes related to Corollary 3.2, see (3.28
Surface Roughness and Hydrodynamic Boundary Conditions
We report results of investigations of a high-speed drainage of thin aqueous
films squeezed between randomly nanorough surfaces. A significant decrease in
hydrodynamic resistance force as compared with predicted by Taylor's equation
is observed. However, this reduction in force does not represents the slippage.
The measured force is exactly the same as that between equivalent smooth
surfaces obeying no-slip boundary conditions, but located at the intermediate
position between peaks and valleys of asperities. The shift in hydrodynamic
thickness is shown to be independent on the separation and/or shear rate. Our
results disagree with previous literature data reporting very large and
shear-dependent boundary slip for similar systems.Comment: Revised versio
Dirichlet problem for Poisson equations in Jordan domains
We study the Dirichlet problem for the Poisson equations △u(z) = g(z) with g ∈ Lp, p > 1, and continuous boundary data φ : ∂D → ℝ in arbitrary Jordan domains D in ℂ and prove the existence of continuous solutions u of the problem.Мы изучаем задачу Дирихле для уравнений Пуассона △u(z) = g(z) с g ∈ Lp, p > 1, и непрерывными граничными данными φ : ∂D → ℝ в произвольных жордановых областях D ⊂ ℂ и доказываем существование непрерывных решений u этой задачи.Ми вивчаємо задачу Дiрихле для рiвнянь Пуасона △u(z) = g(z) с g ∈ Lp, p > 1, та неперервними граничними даними φ : ∂D → ℝ в довiльних жорданових областях D ⊂ ℂ та доводимо iснування неперервних рiшень u цiєї задач
On the theory of the Beltrami equation
We study ring homeomorphisms and, on this basis, obtain a series of theorems on existence of the so-called ring
solutions for degenerate Beltrami equations. A general statement on the existence of solutions for the Beltrami
equations is formulated extending earlier results.Вивчаються кільцеві гомеоморфізми, i на цій підставі отримано низку теорем про існування так званих кільцевих розв'язків вироджених рівнянь Бельтрамі. Сформульовано загальне твердження про існування розв'язків рівнянь Бельтрамі, що узагальнює більш ранні результати
Transcriptional activation and localization of expression of Brassica juncea putative metal transport protein BjMTP1
Peer reviewedPublisher PD
To the theory of semi-linear Beltrami equations
The present paper is devoted to the study of semi-linear Beltrami equations
which are closely relevant to the corresponding semi-linear Poisson type
equations of mathematical physics on the plane in anisotropic and inhomogeneous
media.
In its first part, applying completely continuous ope\-ra\-tors by
Ahlfors-Bers and Leray--Schauder approach, we prove existence of regular
solutions of the semi-linear Beltrami equations with no boundary conditions.
Moreover, here we derive their representation through solutions of the Vekua
type equations and generalized analytic functions with sources.
As consequences, it is given a series of applications of these results to
semi-linear Poisson type equations and to the corresponding equations of
mathematical physics describing such phenomena as diffusion with physical and
chemical absorption, plasma states and stationary burning in anisotropic and
inhomogeneous media.
The second part of the paper contains existence, representation and
regularity results for nonclassical solutions to the Hilbert (Dirichlet)
boundary value problem for semi-linear Beltrami equations and to the Poincare
(Neumann) boundary value problem for semi-linear Poisson type equations with
arbitrary boundary data that are measurable with respect to logarithmic
capacity.Comment: 28 pages. arXiv admin note: text overlap with arXiv:2107.1066
On Dirichlet problem for degenerate Beltrami equations with sources
The present paper is devoted to the study of the Dirichlet problem
as with continuous boundary data
for Beltrami equations ,
a.e., with sources in the case of locally
uniform ellipticity. In this case, we establish a series of effective integral
criteria of the type of BMO, FMO, Calderon-Zygmund, Lehto and Orlicz on
singularities of the equations at the boundary for existence, representation
and regularity of solutions in arbitrary bounded domains of the complex
plane with no boun\-da\-ry component degenerated to a single point
for sources in , , with compact support in . Moreover,
we prove in such domains existence, representation and regularity of weak
solutions of the Dirichlet problem for the Poisson type equation whose source , , has compact
support in and whose mat\-rix valued coefficient guarantees its
locally uniform ellipticity.Comment: 31 pages. arXiv admin note: substantial text overlap with
arXiv:2111.1037
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