On a local geometric property of the generalized elastic transmission eigenfunctions and application

Consider the nonlinear and completely continuous scattering map \[ \mathcal{S}\big((\Omega; \lambda, \mu, V), \mathbf{u}^i\big)=\mathbf{u}_t^\infty(\hat{\mathbf{x}}), \quad \hat{\mathbf{x}}\in\mathbb{S}^{n-1}, \] which sends an inhomogeneous elastic scatterer $(\Omega; V)$ to its far-field pattern $\mathbf{u}_t^\infty$ due incident wave field $\mathbf{u}^i$ via Lam\'e system. Here, $(\lambda, signifies medium configuration of that is compactly supported in $\Omega$. In this paper, we are concerned with intrinsic geometric structure kernel space $\mathcal{S}$, fundamental importance theory inverse invisibility cloaking for waves has received considerable attention recently. It turns out study contained analysing properties a certain non-selfadjoint non-elliptic transmission eigenvalue problem. We propose generalized problem prove eigenfunctions vanish locally around corner $\partial\Omega$ under generic regularity criteria. The criteria characerized by H\"older continuity or Fourier extension property eigenfunctions. As interesting significant application, apply local derive several novel unique identifiability results longstanding single measurement.