Rearrangement inequalities and applications to isoperimetric problems for eigenvalues

Details Rearrangement inequalities and applications to isoperimetric problems for eigenvalues Rearrangement inequalities and applications to isoperimetric problems for eigenvalues

2006-08-05

arxiv.org/abs/math/0608136v1

Mathematics

Analysis of PDEs

Scientific paper

Let $\Omega$ be a bounded $C^{2}$ domain in $\R^n$, and let $\Omega^{\ast}$ be the Euclidean ball centered at 0 and having the same Lebesgue measure as $\Omega$. Consider the operator $L=-\div(A\nabla)+v\cdot \nabla +V$ on $\Omega$ with Dirichlet boundary condition. We prove that minimizing the principal eigenvalue of $L$ when the Lebesgue measure of $\Omega$ 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 $\Omega^*$ with smooth and radially symmetric coefficients. The constraints which are satisfied by the original coefficients in $\Omega$ and the new ones in $\Omega^*$ are expressed in terms of some distribution functions or some integral, pointwise or geometric quantities. Some strict comparisons are also established when $\Omega$ is not a ball.

Affiliated with

Also associated with

No associations

Rating

Rearrangement inequalities and applications to isoperimetric problems for eigenvalues does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Rearrangement inequalities and applications to isoperimetric problems for eigenvalues, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rearrangement inequalities and applications to isoperimetric problems for eigenvalues will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-629440