Asymptotic behavior of spectral functions for elliptic operators with non-smooth coefficients

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,...

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...

Spectral Curves of Operators with Elliptic Coefficients⋆

The classical theory of reduction, initiated by Weierstrass, has found modern applications to the fields of Integrable Systems and Number Theory, to name but two. In this short note we only address specific cases, providing minimal historical references, listing the steps that we devised, and exhibiting some new explicit formulas. A full-length discussion of original motivation, theoretical adv...

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

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions