Rearrangement inequalities and applications to isoperimetric problems for eigenvalues
| dc.creator | Hamel, Francois | |
| dc.creator | Nadirashvili, Nikolai | |
| dc.creator | Russ, Emmanuel | |
| dc.date | 2006-08-05 | |
| dc.date.accessioned | 2026-07-07T07:21:26Z | |
| dc.date.available | 2026-07-07T07:21:26Z | |
| dc.description | Let $Ω$ be a bounded $C^{2}$ domain in $\R^n$, and let $Ω^{\ast}$ be the Euclidean ball centered at 0 and having the same Lebesgue measure as $Ω$. Consider the operator $L=-÷(A\nabla)+v\cdot \nabla +V$ on $Ω$ with Dirichlet boundary condition. We prove that minimizing the principal eigenvalue of $L$ when the Lebesgue measure of $Ω$ is fixed and when $A$, $v$ and $V$ vary under some constraints is the same as minimizing the principal eigenvalue of some operators $L^*$ in the ball $Ω^*$ with smooth and radially symmetric coefficients. The constraints which are satisfied by the original coefficients in $Ω$ and the new ones in $Ω^*$ are expressed in terms of some distribution functions or some integral, pointwise or geometric quantities. Some strict comparisons are also established when $Ω$ is not a ball. | |
| dc.identifier | https://arxiv.org/abs/math/0608136 | |
| dc.identifier | http://arxiv.org/abs/math/0608136 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115299 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35P15, 47A75, 49R50, 35J20 | |
| dc.title | Rearrangement inequalities and applications to isoperimetric problems for eigenvalues | |
| dc.type | text |