Abstract
In this article, an elliptic equation, which type degenerates (either weakly or strongly) at the axis of a 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 exact classical solutions are obtained. The uniqueness of the solutions is proved and the continuity of the solutions on the line of degeneracy is discussed.
Highlights
In this article, an elliptic equation, which type degenerates at the axis of a 3-dimensional cylinder, is considered
This paper is a continuation of [ ] and generalizes Problem D for equation ( ) which is solved in this article
Gi(, φ) =, i =, i.e., the functions gi, i =, do not satisfy all conditions of Theorem under which there exists the solution of Problem D ( ), ( ) continuous at the line of degeneracy r =
Summary
An elliptic equation, which type degenerates (either weakly or strongly) at the axis of a 3-dimensional cylinder, is considered. Problem DA Find the solution ua ∈ C (Q ) ∩ C(Q) of equation ( ) which satisfies the boundary value conditions ua(R, φ, z) = f (φ, z), (φ, z) ∈ S, ( )
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