sg.symplectic geometry – Constant holomorphic strips in Lagrangian floer cohomology

Let $(P,omega)$ be a symplectic manifold , when defining the lagrangian floer cohomology of a pair $(L_0,L_1)$ of lagrangian submanifolds with $Sigma_{L}geq 3$ we will want to look at the space $mathcal{M}_{J}(x,y)$ ,where $x,yin L_0cap L_1$, of $J$-holomorphic strips connecting intersection points and satisfying a sobolev condition, namely that $uin W^{k,2}(mathbb{R}times (0,1), P)$ for $k>1$. Now if we had $x=y$ will the constant strip be an element of $mathcal{M}_{J}(x,x)$? I would say no since we want the paths in this space to satisfy a sobolev in condition ,and in particular the constant path will not satisfy it , but I wanted to make sure this reasoning is correct.

Any enlightment is appreciated , thanks in advance.