Abstracts
Gespeichert in:
| Veröffentlicht in: | Український математичний вісник |
|---|---|
| Datum: | 2019 |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2019
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/169436 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Abstracts // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 148-150. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-169436 |
|---|---|
| record_format |
dspace |
| spelling |
2020-06-13T08:40:32Z 2020-06-13T08:40:32Z 2019 Abstracts // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 148-150. — англ. 1810-3200 https://nasplib.isofts.kiev.ua/handle/123456789/169436 en Інститут прикладної математики і механіки НАН України Український математичний вісник Abstracts Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Abstracts |
| spellingShingle |
Abstracts |
| title_short |
Abstracts |
| title_full |
Abstracts |
| title_fullStr |
Abstracts |
| title_full_unstemmed |
Abstracts |
| title_sort |
abstracts |
| publishDate |
2019 |
| language |
English |
| container_title |
Український математичний вісник |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| issn |
1810-3200 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/169436 |
| citation_txt |
Abstracts // Український математичний вісник. — 2019. — Т. 16, № 1. — С. 148-150. — англ. |
| first_indexed |
2025-11-24T11:20:52Z |
| last_indexed |
2025-11-24T11:20:52Z |
| _version_ |
1850459566093893632 |
| fulltext |
Український математичний вiсник
Том 16 (2019), № 1, 148 – 150
Abstracts
2010 MSC. 30L10
E. S. Afanas’eva, V. V. Bilet. Some properties of quasisymmetries in
metric spaces // Ukrainian Mathematical Bulletin, 16 (2019), No. 1, 1–17.
Let (X, d, µ) and (Y, d′, µ′) be metric spaces α-regular by Ahlfors with α > 0
and locally finite Borel measures µ and µ′, respectively. We consider the class
ACSE of absolutely continuous functions on a.a. compact subsets E ⊂ X and
establish the membership of mappings f : X → Y to a given class.
References. 19
2000 MSC. 30C65, 57Q60, 20F55, 32T99, 30F40, 32H30, 57M30
B. N. Apanasov. Hyperbolic topology and bounded locally
homeomorphic quasiregular mappings in 3-space // Ukrainian
Mathematical Bulletin, 16 (2019), No. 1, 10–27.
We use our new type of bounded locally homeomorphic quasiregular mappi-
ngs in the unit 3-ball to address long standing problems for such mappings,
including the Vuorinen injectivity problem. The construction of such mappings
comes from our construction of non-trivial compact 4-dimensional cobordisms
M with symmetric boundary components and whose interiors have complete 4-
dimensional real hyperbolic structures. Such bounded locally homeomorphic
quasiregular mappings are defined in the unit 3-ball B3 ⊂ R3 as mappi-
ngs equivariant with the standard conformal action of uniform hyperbolic
lattices Γ ⊂ IsomH3 in the unit 3-ball and with its discrete representation
G = ρ(Γ) ⊂ IsomH4. Here, G is the fundamental group of our non-trivial
hyperbolic 4-cobordismM = (H4∪Ω(G))/G, and the kernel of the homomorphi-
sm ρ :Γ → G is a free group F3 on three generators.
References. 26
2010 MSC. 35B40, 35B45, 35J62, 35K59
K. O. Buryachenko. Local sub-estimates of solutions to double phase
parabolic equations via nonlinear parabolic potentials // Ukrainian
Mathematical Bulletin, 16 (2019), No. 1, 28–45.
ISSN 1810 – 3200. c© Iнститут прикладної математики i механiки НАН України
Abstracts 149
For parabolic equations with nonstandard growth conditions, we prove local
boundedness of weak solutions in terms of nonlinear parabolic potentials of the
right-hand side of the equation.
References. 23
2010 MSC. 30C75
I. Denega. Estimates of the inner radii of non-overlapping do-
mains // Ukrainian Mathematical Bulletin, 16 (2019), No. 1, 46–56.
The paper is devoted to extremal problems of the geometric function theory
of complex variable related with estimates of functionals defined on systems of
non-overlapping domains. Till now, many such problems have not been solved,
though some partial solutions are available. In the paper improved method is
proposed for solving problems on extremal decomposition of the complex plane.
The main results of the paper generalize and strengthening some known results
in the theory of non-overlapping domains with free poles to the case of an
arbitrary arrangement of systems of points on the complex plane.
References. 13
2010 MSC. 54E35
O. Dovgoshey, V. Bilet. Uniqueness of spaces pretangent to metric
spaces at infinity // Ukrainian Mathematical Bulletin, 16 (2019), No. 1,
57–87.
We find the necessary and sufficient conditions under which an unbounded
metric space X has, at infinity, a unique pretangent space ΩX
∞,r̃ for every scaling
sequence r̃. In particular, it is proved that ΩX
∞,r̃ is unique and isometric to the
closure of X for every logarithmic spiral X and every r̃. It is also shown that
the uniqueness of pretangent spaces to subsets of a real line is closely related to
the “asymptotic asymmetry” of these subsets.
References. 12
2010 MSC. 42A10, 42B99
M. V. Hembars’kyi, S. B. Hembars’ka. Approximate characteristics of
the classes BΩ
p,θ of periodic functions of one variable and many ones //
Ukrainian Mathematical Bulletin, 16 (2019), No. 1, 88–104.
We obtained the exact-by-order estimates of some approximate characteri-
stics of classes of the Nikol’skii–Besov type of periodic functions of one variable
and many ones in the space B∞,1 such that the norm in it is not weaker than
the L∞-norm.
References. 20
150 Abstracts
2010 MSC. Primary 30C62, 31A05, 31A20, 31A25, 31B25, 35J61
Secondary 30E25, 31C05, 34M50, 35Q15
V. Gutlyanskĭı, O. Nesmelova, V. Ryazanov. To the theory of semi-linear
equations in the plane // Ukrainian Mathematical Bulletin, 16 (2019), No. 1,
105–140.
In two dimensions, we present a new approach to the study of the semi-
linear equations of the form div[A(z)∇u] = f(u), the diffusion term of which is
the divergence uniform elliptic operator with measurable matrix functions A(z),
whereas its reaction term f(u) is a continuous non-linear function. Assuming
that f(t)/t→ 0 as t→ ∞, we establish a theorem on existence of weak C(D)∩
W 1,2
loc
(D) solutions of the Dirichlet problem with arbitrary continuous boundary
data in any bounded domains D without degenerate boundary components. As
consequences, we give applications to some concrete model semi-linear equations
of mathematical physics, arising from modelling processes in anisotropic and
inhomogeneous media. With a view to further development of the theory of
boundary value problems for the semi-linear equations, we prove a theorem
on the solvability of the Dirichlet problem for the Poisson equation in Jordan
domains with arbitrary boundary data that are measurable with respect to the
logarithmic capacity.
References. 74
V. A. Zorich. To the theory of quasiconformal mappings // Ukrainian
Mathematical Bulletin, 16 (2019), No. 1, 141–147.
The open questions of the theory of quasiconformal mappings that are
adjacent to the field of studies of Professor Bogdan Bojarski are discussed.
References. 16
|