All self-adjoint extensions of the magnetic Laplacian in nonsmooth domains and gauge transformations

We use boundary triples to find a parametrization of all self-adjoint extensions the magnetic Schrodinger operator, in quasi-convex domain~$\Omega$ with compact boundary, and potentials components $\textrm{W}^{1}_{\infty}(\overline{\Omega})$. This gives also new characterization Laplacian nonregular domains. Then we discuss gauge transformations for such generalize equivalence Dirichlet operator Laplacian; relation Aharonov-Bohm effect, including irregular solenoids, is discussed. In particular, case (bounded) domains it shown that if some extension unitarily equivalent (through multiplication by smooth unit function) realization zero potential, then same occurs realizations.