Spectral asymptotics for elliptic second order differential operators

Lp SPECTRAL THEORY OF HIGHER-ORDER ELLIPTIC DIFFERENTIAL OPERATORS

Spectral Asymptotics for Dirichlet Elliptic Operators with Non-smooth Coefficients

We consider a 2m-th-order elliptic operator of divergence form in a domain  of Rn, assuming that the coefficients are Hölder continuous of exponent r 2 (0, 1]. For the self-adjoint operator associated with the Dirichlet boundary condition we improve the asymptotic formula of the spectral function e( 2m , x , y) for x = y to obtain the remainder estimate O( n + dist(x , ) 1 n 1) with any 2 (0,...

Kernel Asymptotics of Exotic Second-Order Operators

The Navier–Lamé operator of classical elasticity, μ∆v+(λ+μ)∇(∇·v), is the simplest example of a linear differential operator whose second-order terms involve a coupling among the components of a vector-valued function. Similar operators on Riemannian manifolds arise in conformal geometry and in quantum gravity. (In the latter context they have come to be called “nonminimal”, but “exotic” is pro...

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

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...