Displaying similar documents to “Riemann-type boundary value problems for bicircular domains with a boundary condition containing partial derivatives.”

On propagation of boundary continuity of holomorphic functions of several variables

Salla Franzén, Burglind Jöricke (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We prove that continuity properties of bounded analytic functions in bounded smoothly bounded pseudoconvex domains in two-dimensional affine space are determined by their behaviour near the Shilov boundary. Namely, if the function has continuous extension to an open subset of the boundary containing the Shilov boundary it extends continuously to the whole boundary. If it is Hölder continuous on such a boundary set, it is Hölder continuous on the closure of the domain. The statements...

A note on the solvability of homogeneous Riemann boundary problem with infinity index

Juan Bory-Reyes (2021)

Communications in Mathematics

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In this note we establish a necessary and sufficient condition for solvability of the homogeneous Riemann boundary problem with infinity index on a rectifiable open curve. The index of the problem we deal with considers the influence of the requirement of the solutions of the problem, the degree of non-smoothness of the curve at the endpoints as well as the behavior of the coefficient at these points.

Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities

P. Ch. Tsamatos (2004)

Annales Polonici Mathematici

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We study a nonlocal boundary value problem for the equation x''(t) + f(t,x(t),x'(t)) = 0, t ∈ [0,1]. By applying fixed point theorems on appropriate cones, we prove that this boundary value problem admits positive solutions with slope in a given annulus. It is remarkable that we do not assume f≥0. Here the sign of the function f may change.

On the connectedness of boundary and complement for domains

Andrzej Czarnecki, Marcin Kulczycki, Wojciech Lubawski (2011)

Annales Polonici Mathematici

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This article gives a short and elementary proof of the fact that the connectedness of the boundary of an open domain in ℝⁿ is equivalent to the connectedness of its complement.