Exact solutions of Dirichlet type problem to elliptic equation, which type degenerates at the axis of cylinder. I

Boundary value problems

Stasys Rutkauskas¹ 

[1] Institute of Mathematics and Informatics of Vilnius University, Vilnius, Lithuania

关键词: degenerate elliptic equations;    boundary value problems;    Dirichlet type problem;   

DOI  :  10.1186/s13661-016-0690-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY