Coupled boundary condition
= Coupled boundary condition
A linear <boundary condition> can relate traces at different endpoints rather than prescribe data independently at each endpoint. For a second-order <differential equation>, examples are $a_1y(a)+b_1y'(a)+c_1y(b)+d_1y'(b)=0$ together with another independent relation. The resulting <operator domain> determines whether the boundary form vanishes. Coupling by itself guarantees neither <self-adjointness> nor its failure.