On the Dirichlet Problem to Elliptic Equation, the Order of which Degenerates at the Axis of a Cylinder. Issue 5 (3rd September 2017)

• Record Type: Journal Article
• Authors: Rutkauskas, Stasys
• Is Part Of: Mathematical modelling and analysis. Volume 22:Issue 5(2017)
• Page Start: 717
• Page End: 732
• Publication Date: 2017-09-03
• Subjects: boundary value problems -- degenerate -- elliptic equation -- second-order equation; 35J70; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2017.1362053
• Languages: English
• ISSNs: 1392-6292

Abstract

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.