In this paper second order elliptic boundary value problems on bounded domains Ω ⊂ Rn with boundary conditions on ∂Ω depending nonlinearly on the spectral parameter are investigated in an operator theoretic framework. For a general class of locally meromorphic functions in the boundary condition a solution operator of the boundary value problem is constructed with the help of a linearization pr...

We concentrate on a model diffusion equation on a Lipschitz simply connected bounded domain with a small diffusion coef£cient in a Lipschitz simply connected subdomain located strictly inside of the original domain. We study asymptotic properties of the solution with respect to the small diffusion coef£cient vanishing. It is known that the solution asymptotically turns into a solution of a corr...

Vector-valued elliptic and parabolic boundary value problems subject to general boundary conditions have been investigated recently in [DHP01] in the Lp-context for 1 < p < 1. One of the main goals of this paper was to deduce a maximal Lp-regularity result for the solution of the parabolic initial boundary value problem. A classical reference in the elliptic context are the celebrated papers of...

We prove the existence of strong solutions to a class of inhomogeneous boundary-value problems for an elliptic-hyperbolic equation. The equation is an arbitrarily small lower-order perturbation of an equation that arises in the linearization of an approximate model for high-frequency waves near a caustic. The domain boundary is allowed to extend into both the elliptic and hyperbolic regions of ...