Spectral analysis of Dirac operators with delta interactions supported on the boundaries of rough domains

Given an open set $\Omega\subset\mathbb{R}^3$. We deal with the spectral study of Dirac operators form $H_{a,\tau}=H+A_{a,\tau}\delta_{\partial\Omega}$, where $H$ is free operator in $\mathbb{R}^3$, $A_{a,\tau}$ a bounded invertible, self-adjoint $\mathit{L}^{2}(\partial\Omega)^4$, depending on parameters $(a,\tau)\in\mathbb{R}\times\mathbb{R}^n$, $n\geqslant1$. investigate self-adjointness and related properties $H_{a,\tau}$, such as phenomenon confinement Sobolev regularity domain different situations. Our techniques, which based fundamental solutions layer potentials, allows us to tackle above problems under mild geometric measure theoretic assumptions $\Omega$.