Abstract:
We consider strongly elliptic differential-difference equations with mixed boundary conditions in a bounded domain. There are homogeneous Dirichlet conditions on a part of the boundary, and boundary conditions of the third kind on the other part of the boundary. We establish the connection between these problems and nonlocal mixed problems for strongly elliptic differential equations. We prove the uniqueness and the smoothness of their solutions.
Keywords:differential-difference equation, elliptic equation, mixed boundary conditions, Dirichlet boundary conditions, boundary conditions of the third kind.
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