Elliptic Equations with Critical Growth and a Large Set of Boundary Singularities
| dc.creator | Ghoussoub, Nassif | |
| dc.creator | Robert, Frederic | |
| dc.date | 2005-08-18 | |
| dc.date.accessioned | 2026-07-07T05:22:28Z | |
| dc.date.available | 2026-07-07T05:22:28Z | |
| dc.description | We solve variationally certain equations of stellar dynamics of the form $-\sum_i\partial_{ii} u(x) =\frac{|u|^{p-2}u(x)}{{\rm dist} (x,{\mathcal A} )^s}$ in a domain $Ω$ of $\rn$, where ${\mathcal A} $ is a proper linear subspace of $\rn$. Existence problems are related to the question of attainability of the best constant in the following recent inequality of Badiale-Tarantello [1]: $$0<μ_{s,¶}(Ω)=\inf{\int_Ω|\nabla u|^2 dx; u\in \huno \hbox{and}\int_Ω\frac{|u(x)|^{\crit(s)}}{|π(x)|^s} dx=1}$$ where $0<s<2$, $\crit(s)=\frac{2(n-s)}{n-2}$ and where $π$ is the orthogonal projection on a linear space $¶$, where $\hbox{dim}_{\rr}¶\geq 2$. We investigate this question and how it depends on the relative position of the subspace $\Porth$, the orthogonal of $¶$, with respect to the domain $Ω$ as well as on the curvature of the boundary $\partialΩ$ at its points of intersection with $\Porth $. | |
| dc.description | 27 pages. Updated versions --if any-- of this author's papers can be downloaded at http://www.pims.math.ca/~nassif/ | |
| dc.identifier | https://arxiv.org/abs/math/0508348 | |
| dc.identifier | http://arxiv.org/abs/math/0508348 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76075 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Elliptic Equations with Critical Growth and a Large Set of Boundary Singularities | |
| dc.type | text |