Homogenization of the higher-order Schrödinger-type equations with periodic coefficients
Homogenization of the higher-order Schrödinger-type equations with periodic coefficients
In $L\_2(\mathbb{R}^d;\mathbb{C}^n)$, we consider a matrix strongly elliptic differential operator $A\_\varepsilon$ of order $2p$, $p \geqslant 2$. The operator $A\_\varepsilon$ is given by $A\_\varepsilon = b(\mathbf{D})^\* g(\frac{\mathbf{x}}{\varepsilon}) b(\mathbf{D})$, $\varepsilon >0$, where $g(\mathbf{x})$ is a periodic, bounded, and positive definite matrix-valued function, and $b(\mathbf{D})$ is a homogeneous differential operator of order …