Specifically, I have $Lu=f$, where $L$ is a linear elliptic pseudodifferential operator, on an unbounded domain of the form $\Omega\times [0,\infty)$, $\Omega$ has Lipschitz boundary, $u$ is 0 on all boundaries, i.e. $(\partial\Omega\times[0,\infty))$ $\cup$ $(\Omega\times\{0\})$. I imagine that there are existence theorems that contain this problem as a special case, but the results I have found deal with bounded domains.
