4 papers · 1 filter
The Dirichlet problem for semi-linear equations
Vladimir Gutlyanskii, Olga Nesmelova, Vladimir Ryazanov
We study the Dirichlet problem for the semi--linear partial differential equations in simply connected domains of the complex plane wi…
Toward the theory of semi-linear equations
Vladimir Gutlyanskii, Olga Nesmelova, Vladimir Ryazanov
In this paper we study the semilinear partial differential equations in the plane the linear part of which is written in a divergence form. The main result is given as a factorizat…
Ring homeomorphisms and prime ends
Vladimir Gutlyanskii, Vladimir Ryazanov, Eduard Yakubov
We show that every homeomorphic solution of a Beltrami equation in a domain is the so--called ring $…
On -conformal homeomorphisms and boundary correspondence
Vladimir Gutlyanskii, Ken-ichi Sakan, Toshiyuki Sugawa
We study the boundary correspondence under -homeomorphisms of the open upper half-plane onto itself. Sufficient conditions are given for to admit a homeomorphic extensio…