Homogenization of high order elliptic operators with periodic coefficients

Exponential Homogenization of Linear Second Order Elliptic PDEs with Periodic Coefficients

A problem of homogenization of a divergence-type second order uniformly elliptic operator is considered with arbitrary bounded rapidly oscillating periodic coefficients, either with periodic “outer” boundary conditions or in the whole space. It is proved that if the right-hand side is Gevrey regular (in particular, analytic), then by optimally truncating the full two-scale asymptotic expansion ...

Periodic homogenization of Dirichlet problem for divergence type elliptic operators

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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 In this short note we only address specific cases, providing minimal historical references, listing the steps that we devised, and exhibiting some new explicit formulas.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...

Periodic Homogenization of Elliptic Problems (Draft)