A remark on elliptic differential equations on manifold
Copyright policy )A remark on elliptic differential equations on manifold
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 DirichletBitsadze-Samarskii type nonlocal boundary value problem on manifolds, in H¨older spaces. In addition, in various H¨older norms, it establishes new coercivity inequalities for solutions of such elliptic nonlocal type boundary value problems on smooth manifolds.
QA299.6-433, Differential equations on manifolds, QA801-939, Analytic mechanics, көпбейнедегi дифференциалдық теңдеу, корректность, Boundary-Value-Problems, Well posedness, Well-Posedness, QA273-280, 510, корректiлiгi, well-posedness, self adjoint positive definite operator, самосопряженный положительно определенный оператор, дифференциальные уравнения на многообразиях, self-adjoint positive definite operator, өзiне өзi түйiндес оң анықталған оператор, Probabilities. Mathematical statistics, differential equations on manifolds, Analysis
QA299.6-433, Differential equations on manifolds, QA801-939, Analytic mechanics, көпбейнедегi дифференциалдық теңдеу, корректность, Boundary-Value-Problems, Well posedness, Well-Posedness, QA273-280, 510, корректiлiгi, well-posedness, self adjoint positive definite operator, самосопряженный положительно определенный оператор, дифференциальные уравнения на многообразиях, self-adjoint positive definite operator, өзiне өзi түйiндес оң анықталған оператор, Probabilities. Mathematical statistics, differential equations on manifolds, Analysis
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