On the Dirichlet Problem to Elliptic Equation, the Order of which Degenerates at the Axis of a Cylinder

Abstract

In this article, an elliptic equation, which type degenerates (either weakly or strongly) at the axis of 3-dimensional cylinder, is considered. The statement of a Dirichlet type problem in the class of smooth functions is given and, subject to the type of degeneracy, the classical solutions are composed. The uniqueness of the solutions is proved and the continuity of the solutions on the line of degeneracy is discussed.

Keywords:

• boundary value problems
• degenerate
• elliptic equation
• second-order equation

AMS Subject Classification:

• 35J70