most recent 30 from http://mathoverflow.net 2013-05-21T20:12:56Z http://mathoverflow.net/feeds/question/51771 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/51771/existence-of-solution-for-poisson-problem-with-pure-neumann-bcs Mihai 2011-01-11T15:28:21Z 2011-01-15T05:13:57Z

<p>Hello all,</p> <p>Does the following boundary value problem admit unique solutions $q$:</p> <p>$- \Delta q + \beta q = f$, $x \in \Omega$</p> <p>$ \nabla q \cdot \vec{n} = g $, $x \in \Gamma := \partial \Omega$,</p> <p>where $\beta > 0$ is reasonably small? I am not clear if the pure Neumann boundary conditions make the solution non-unique; does the inhomogeneity in the volume equation take care of this problem? What are the spaces for $f$ and $g$ such that we have uniqueness?</p>