Can I read Logarithmic Potential and Generalized Analytic Functions on EtoBox?

Logarithmic Potential and Generalized Analytic Functions by V. Gutlyanskiĭ; O. Nesmelova; V. Ryazanov; A. Yefimushkin is a scholarly article available to read on EtoBox.

What is Logarithmic Potential and Generalized Analytic Functions about?

The study of the Dirichlet problem in the unit disk D with arbitrary measurable data for harmonic functions is due to the famous dissertation of Luzin [31]. Later on, the known monograph of Vekua [48] has been devoted to boundary-value problems (only with Hölder continuous data) for the generalized analytic functions, i.e., continuous complex valued functions h(z) of the complex variable z = x + iy with generalized first partial derivatives by Sobolev satisfying equations of the form ∂zh + ah + bh = c , where it was assumed that the complex valued functions a, b and c belong to the class L p with some p > 2 in smooth enough domains D in C. The present paper is a natural continuation of our previous articles on the Riemann, Hilbert, Dirichlet, Poincaré and, in particular, Neumann boundary-value problems for quasiconformal, analytic, harmonic, and the so-called A-harmonic functions with boundary data that are measurable with respect to logarithmic capacity. Here, we extend the corresponding results to the generalized analytic functions h : D → C with the sources g : ∂zh = g ∈ L p , p > 2 , and to generalized harmonic functions U with sources G : This paper contains various theorems o

Author

V. Gutlyanskiĭ; O. Nesmelova; V. Ryazanov; A. Yefimushkin

Publisher

Springer Science and Business Media LLC

Published

2021

Language

EN