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We consider the scattering problem governed by the Helmholtz equation withinhomogeneity in both `conductivity' in the divergence form and `potential' inthe lower order term. The support of the inhomogeneity is assumed to contain aconvex corner. We prove that, due to the presence of such corner underappropriate assumptions on the potential and conductivity in the vicinity ofthe corner, any incident field scatters. Based on corner scattering analysis wepresent a uniqueness result on determination of the polygonal convex hull ofthe support of admissible inhomogeneities, from scattering data correspondingto one single incident wave. These results require only certain regularityaround the corner for the coefficients modeling the inhomogeneity, whereas awayfrom the corner they can be quite general. Our main results on scattering andinverse scattering are established for $\mathbb{R}^2$, while some analytictools are developed in any dimension $n\geq 2$.

On Corner Scattering for Operators of Divergence Form and Applications to Inverse Scattering