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Öğe On bitsadze-samarskii type elliptic differential problems on hyperbolic plane(Academic Publications Ltd., 2021) Ashyralyev, A.; Sozen, Y.; Hezenci, F.In the present article, we consider nonlocal boundary value problems (NBVP) of elliptic type on relatively compact domains in the hyperbolic plane. We establish the wellposedness of Neumann-Bitsadze-Samarskii type and also Dirichlet-Bitsadze-Samarskii type on such domains. Furthermore, we establish new coercivity inequalities for solutions of such elliptic NBVP on relatively compact domains in the hyperbolic plane with various H¨older norms. © 2021Öğe A remark on elliptic differential equations on manifold(Karaganda State Univ, 2020) Ashyralyev, A.; Sozen, Y.; Hezenci, F.For elliptic boundary value problems of nonlocal type in Euclidean space, the well posedness has been studied by several authors and it has been well understood. On the other hand, such kind of problems on manifolds have not been studied yet. Present article considers differential equations on smooth closed manifolds. It establishes the well posedness of nonlocal boundary value problems of elliptic type, namely Neumann-Bitsadze-Samarskii type nonlocal boundary value problem on manifolds and also Dirichlet-Bitsadze-Samarskii type nonlocal boundary value problem on manifolds, in Holder spaces. In addition, in various Holder norms, it establishes new coercivity inequalities for solutions of such elliptic nonlocal type boundary value problems on smooth manifolds.
