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

Abstract

© 2019, African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature. 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.