The paper considers the abstract nonlocal boundary value problem for elliptic-parabolic equations:
in a Hilbert space , with the self-adjoint positive definite operator .
By is denoted the Banach space of all continuous functions defined on with values in , equipped with the norm .
By , , is denoted the Banach space obtained by completion of the set of all smooth -valued functions on in the norm
In the main theorem, under some conditions, the well-posedness of the boundary value problem (1) in a Hölder space is established and coercive stability estimates for the solutions are obtained.
Later, some applications of this theorem to the mixed boundary value problems for elliptic-parabolic equations are given.