Vanishing solution of the Poisson equation at infinity - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T03:10:28Z http://mathoverflow.net/feeds/question/57258 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/57258/vanishing-solution-of-the-poisson-equation-at-infinity Vanishing solution of the Poisson equation at infinity Patrícia Cunha 2011-03-03T15:46:17Z 2011-03-03T15:46:17Z <p>Hi, I am interested in finding some vanish bahavior at infinity of the solutions of this kind of equations:</p> <p>$-\Delta\phi+a(x)\phi=b(x)$</p> <p>where $a(x), b(x)\in L^{p}$ with $1\leq p\leq 3$. Besides $\phi\in\mathcal{D}^{1,2}(\mathbb{R}^3)$ which is the completion of $C_0^{\infty}(\mathbb{R}^3)$ with respect to the norm $\|\phi\|_{\mathcal{D^{1,2}}}^2=\int|\nabla u|^2$.</p> <p>Well, I think that using Potential Theory I can get this kind of property for the Poisson equation, and then mabye the same is true for my problem. </p> <p>Any ideas are welcame.</p>