Abstract: This paper presents a self-adjointness condition for the operator F appearing in the Beinstein energy integral and explains the difference between this condition and the conservation condition of the system.Conventional solid-wall boundary conditions can maintain the conservation of a system and thereby guarentee the self-adjointness of the operator F,whereas conditions on moving boundaries can only achieve the self-adjointness of the operator F at most.While stipulating the boundary conditions,special attentions must be paid not only to achieving the self-adjointness of the operator F so as to make the energy principle valid,but also to the physical basis of the boundary conditions so as to make the stability judgement meaningful.