Maximal regularity properties of Agranovich-Vishik type abstract elliptic operators in the half-plane

Strongly Elliptic Second-Order Systems with Boundary Conditions on a Nonclosed Lipschitz Surface∗

We consider boundary value problems and transmission problems for strongly elliptic second-order systems with boundary conditions on a compact nonclosed Lipschitz surface S with Lipschitz boundary. The main goal is to find conditions for the unique solvability of these problems in the spaces H , the simplest L2-spaces of the Sobolev type, with the use of potential type operators on S . We also ...

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

properties of M−hyoellipticity for pseudo differential operators

In this paper we study properties of symbols such that these belong to class of symbols sitting insideSm ρ,φ that we shall introduce as the following. So for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of M−hypoelliptic pseudodifferential operators for which define base on this class of symbols. Also we consider maxi...

Boundary Value Problems for a Class of Elliptic Operator Pencils

In this paper operator pencils A(x,D, λ) are studied which act on a manifold with boundary and satisfy the condition of N-ellipticity with parameter, a generalization of the notion of ellipticity with parameter as introduced by Agmon and Agranovich–Vishik. Sobolev spaces corresponding to the Newton polygon are defined and investigated; in particular it is possible to describe their trace spaces...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators