On periodic boundary value problems with an inclined derivative for a second-order elliptic equation

Batirkhan Turmetov, Maira D. Koshanova, Moldir A. Muratbekova

2021

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DOI 10.1063/5.0040263
Data confidence 70 medium
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Abstract

In this paper, we study solvability of new classes of nonlocal boundary value problems for second-order elliptic type equation. The considered problems are multidimensional analogues (in the case of circular regions) of classical periodic boundary value problems in rectangular domains. To study the main problem, first, an auxiliary boundary value problem with inclined derivative is considered for the second order elliptic equation. The main problems are solved by reducing them to a sequential solution of the Dirichlet problem and the problem with inclined derivative. Theorems on existence and uniqueness of a solution of the problems are proved.