Krein's Resolvent Formula for Self-Adjoint Extensions of Symmetric   Second Order Elliptic Differential Operators
  Given a symmetric, semi-bounded, second order elliptic differential operator on a bounded domain with $C^{1,1}$ boundary, we provide a Krein-type formula for the resolvent difference between its Friedrichs extension and an arbitrary self-adjoint one. 
Andrea Posilicano, Luca Raimondi