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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.

Infinite dimension of solutions of the Dirichlet problem

88%

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.

Ograniczanie wyników

2 Open Mathematics

2 Ryazanov V.

1 2016

1 2015

Wyniki wyszukiwania

On the Riemann-Hilbert problem in multiply connected domains

Infinite dimension of solutions of the Dirichlet problem