most recent 30 from http://mathoverflow.net 2013-06-19T02:28:40Z http://mathoverflow.net/feeds/question/63743 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/63743/existence-of-solutions-to-elliptic-pde-in-undbounded-domain Max 2011-05-02T21:26:57Z 2011-05-02T21:26:57Z

<p>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.</p>