Resolvent estimates of elliptic differential and finite-element operators in pairs of function spaces

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...

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

Resolvent Estimates for Elliptic Finite Element Operators in One Dimension

We prove the analyticity (uniform in h ) of the semigroups generated on Lp(0, 1), 1 < p < oo , by finite element analogues Ah of a onedimensional second-order elliptic operator A under Dirichlet boundary conditions. This is accomplished by showing the appropriate estimates for the resolvents by means of energy arguments. The results are applied to prove stability and optimal-order error bounds ...

Strong convergence theorem for finite family of m-accretive operators in Banach spaces

The purpose of this paper is to propose a compositeiterative scheme for approximating a common solution for a finitefamily of m-accretive operators in a strictly convex Banach spacehaving a uniformly Gateaux differentiable norm. As a consequence,the strong convergence of the scheme for a common fixed point ofa finite family of pseudocontractive mappings is also obtained.

Asymptotic distribution of eigenvalues of the elliptic operator system

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.