In this paper we prove parameter-dependent a priori estimates for mixed-order boundary value problems of rather general structure. In particular, the diagonal operators are not assumed to be of the same order. Our assumptions on the structure of the boundary value problem covers the case of Dirichlet type boundary conditions.

It is proved that the first eigenfunction of the mixed boundary-value problem for the Laplacian in a thin domain Ωh is localized either at the whole lateral surface Γh of the domain, or at a point of Γh, while the eigenfunction decays exponentially inside Ωh. Other effects, attributed to the high-frequency range of the spectrum, are discussed for eigenfunctions of the mixed boundary-value and N...

In this paper, we study a second order differential operator with mixed nonlocal boundary conditions combined weighting integral boundary condition with another two point boundary condition. Under certain conditions on the weighting functions and on the coefficients in the boundary conditions, called non regular boundary conditions, we prove that the resolvent decreases with respect to the spec...