An efficient abstract method for the study of an initial boundary value problem on singular domain

• Published in: Afrika mathematica Vol. 30; no. 3-4; pp. 551 - 562
• Main Authors: Chaouchi, Belkacem, Kostić, Marko
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2019; Springer Nature B.V
• Subjects: Applications of Mathematics; Boundary value problems; Differential equations; History of Mathematical Sciences; Mathematics; Mathematics and Statistics; Mathematics Education; 34K30; Abstract differential equations of second order; Variable operator coefficients; 34G10; 47D03; Hölder spaces; 35J25; Anti-periodic boundary conditions
• ISSN: 1012-9405; 2190-7668
• DOI: 10.1007/s13370-019-00665-4

The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract differential equation with variable operators coefficients subject to some anti-periodic conditions. The complete study of this abstract version allows us to establish some interesting regularity results for our problem. The study is performed in the framework of Hölder spaces.