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Inequality involving sobolev spaces

Just take a derivative, and you get $$ i \lambda u_x = f_x - w_x $$ So taking the $L^2(-L,0)$ norms on both sides, you get $$ \lambda^2 \int |u_x|^2 \leq \int |f_x - w_x|^2 $$ The RHS can be expanded ...
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