Large-domain decay conjecture for mixed normal-superconducting states

Let $\Omega$ be the domain, let $B_n$ be the normal-state magnetic field, and let Proposition provide the conditions under consideration. For a compact set $K\subset\Omega\setminus B_n^{-1}(0)$, consider the estimate denoted by. Large-domain decay conjecture. Under the conditions of Proposition, for any compact set $K\subset\Omega\setminus B_n^{-1}(0)$, there exist $R_0>0$, $C>0$, and $\alpha>0$ such that for any $R>R_0$, the estimate is satisfied. This conjecture is presented as a strengthening of Proposition, concerning the behavior of the mixed normal-superconducting state in the large-domain limit; the supplied text does not establish whether it has been proved or remains open.