G. Makatsaria

Correct Boundary Value Problems for Some Classes of Singular Elliptic Differential Equations on a Plane

abstract:
The investigation of differential equations of the type
$$
\frac{\pa^n\om}{\pa\ol{z}^n}+a_{n-1}\frac{\pa^{n-1}\om}{\pa\ol{z}^{n-1}}+ a_{n-2}\frac{\pa^{n-2}\om}{\pa\ol{z}^{n-2}}+\cdots+a_0\om=0
$$
with sufficiently smooth coefficients $a_0,a_1,\dots,a_{n-1}$ (the theory of meta-analytic functions) traces back to the work of G. Kolosov [6]. Subsequently, a vast number of papers in this direction were published by many authors. The present work deals with some singular cases of the above-given equation. Correct boundary value problems are pointed out, and their in a sense complete analysis is given.

Mathematics Subject Classification: 30E25, 30G20

Key words and phrases: Meta-analytic functions, singular, elliptic, differential, equation, correct, boundary, problems