  We prove that for any compact Lagrangian submanifold intersecting an open
subset $U$ in tame symplectic manifold $(M,\omega)$, the Hofer displacement
energy of $L$ from $U$ is positive, provided $L \cap U \neq \emptyset$. We also
give an explicitlower bound in terms of an $\epsilon$-regularity type invariant
for pseudo-holomorphic curves relative to $L$.
