Abstract
We consider, in a Hilbert space H, a problem on [0,1] for a second order elliptic operator-differential equation with operator-boundary conditions. We also consider second order elliptic differential equations with operatorboundary conditions in cylindrical domains in the case when operator-boundary conditions contain integral terms over the whole domain. In this case, the proof of the density of the domain of definition of operators in a space is difficult. When boundary conditions are local, this fact is a simple corollary of the density ofC ∞0 (Ω) inL p (Ω).
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Yakubov, S. Problems for elliptic equations with operator-boundary conditions. Integr equ oper theory 43, 215–236 (2002). https://doi.org/10.1007/BF01200254
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DOI: https://doi.org/10.1007/BF01200254