On a Dirichlet problem for one improperly elliptic equation

Abstract

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 the homogeneous problem and the number of linearly independent solvability conditions of the inhomogeneous problem are determined. Solutions of the homogeneous problem and solvability conditions of the inhomogeneous problem are obtained in explicit form.

COMMUNICATED BY:

• H. Begehr

Keywords:

• Dirichlet problem
• correct boundary value problem
• defect numbers
• improperly elliptic equation

AMS SUBJECT CLASSIFICATIONS:

• Primary: 35J40
• Secondary: 35J58
• 35J30
• 30G20