Wyniki wyszukiwania - Biblioteka Nauki

Nowa wersja platformy, zawierająca wyłącznie zasoby pełnotekstowe, jest już dostępna.
Przejdź na https://bibliotekanauki.pl

Ograniczanie wyników

Znaleziono wyników: 3

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Infinite dimension of solutions of the Dirichlet problem

100%

Ryazanov V.

Open Mathematics

2015

tom 13

nr 1

It is proved that the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e. has the infinite dimension.

On the Riemann-Hilbert problem in multiply connected domains

100%

Ryazanov V.

Open Mathematics

2016

tom 14

nr 1

13-18

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 limits. Furthermore, it is shown that the dimension of the spaces of these solutions is infinite.

On a theorem of Lindelof

51%

Gutlyanskii V. Y. , Martio O. , Ryazanov V.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2011

tom 65

nr 2

We give a quasiconformal version of the proof for the classical Lindelof theorem: Let \(f\) map the unit disk \(\mathbb{D}\) conformally onto the inner domain of a Jordan curve \(\mathcal{C}\): Then \(\mathcal{C}\) is smooth if and only if arg \(f'(z)\) has a continuous extension to \(\overline{\mathbb{D}}\). Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.