To read the full-text of this research, you can request a copy directly from the authors.
Abstract
The paper considers the properly elliptic equation in multiply connected domains. An effective solution of Dirichlet problem is proposed by reduction to Fredholm integral equation of the second kind. Conditions ensuring unique solvability are derived.
The Dirichlet problem for sixth order improperly elliptic equation is considered. The functional class of boundary functions, where this problem is normally solvable is determined. If the roots of the characteristic equation satisfy some conditions, the number of linearly independent solutions of homogeneous problem and the number of linearly independent solvability conditions of in-homogeneous problem are obtained. Solutions of homogeneous problem and solvability conditions of in-homogeneous problem are obtained in explicit form.
The Dirichlet problem for a class of properly elliptic sixth-order equations in the unit disk is considered. Formulas for determining the defect numbers of this problem are obtained. Linearly independent solutions of the homogeneous problem and conditions for the solvability of the inhomogeneous problem are given explicitly.
ResearchGate has not been able to resolve any references for this publication.