An efficient abstract method for the study of an initial boundary value problem on singular domain
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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.
KeywordsAbstract differential equations of second order Variable operator coefficients Anti-periodic boundary conditions Hölder spaces
Mathematics Subject Classification34G10 34K30 35J25 47D03
The second named author is partially supported by Grant 174024 of Ministry of Science and Technological Development, Republic of Serbia.