## A characterization of the non-local boundary value problems associated with an elliptic operator |

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algebraically and topologically assumption Au,v Au)w boundary condition boundary differential operators boundary operators boundary value problems bounded sesquilinear form C D(a closable closed operator closed subspace contained Corollary 2.1 correspond to T:V D(Aq Definition dissipative operators domain elliptic operator equivalent essential spectrum follows formally selfadjoint Fredholm operator graphtopology Green's formula H^fi Hilbert space HS(fi HS(n HS(r implies integer isomorphism Lemma Let A correspond Let u e linear Lions-Magenes 26 lower bounded operator lower bounded sesquilinear Math maximal lower bounded maximal nonnegative maximal positive Neumann condition norm nullspace numerical range operator L:X properties Proposition proved regularly lower bounded regularly nonnegative regularly positive Remark represents a Neumann represents the Neumann satisfies selfadjoint operator sense of Corollary subset subspace of Z(A Theorem 2.1 theory topological sum trace class u e D(A u,v e unique v e D(A z e D(T