A new type of CGO solutions and its applications in corner scattering

We consider corner scattering for the operator $\nabla \cdot \gamma(x)\nabla +k^2\rho(x)$ in $\mathbb{R}^2$, with $\gamma$ a positive definite symmetric matrix and $\rho$ scalar function. A is referred to one that on boundary of (compact) support $\gamma(x)-I$ or $\rho(x)-1$, where $I$ stands identity matrix. assume function small neighborhood corner. show any admissible incident field will be scattered by such corners, which are allowed concave. Moreover, we provide brief discussion existence non-scattering waves when $\gamma-I$ has jump across In order prove results, construct new type complex geometric optics (CGO) solutions.