On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms

Details On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms

2005-03-05

arxiv.org/abs/math/0503097v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 1, February 2005, pp. 93-102

Mathematics

Analysis of PDEs

10 pages

Scientific paper

Let $B_1$ be a ball of radius $r_1$ in $S^n(\Hy^n)$, and let $B_0$ be a smaller ball of radius $r_0$ such that $\bar{B_0}\subset B_1$. For $S^n$ we consider $r_1< \pi$. Let $u$ be a solution of the problem $-\La u =1$ in $\Om := B_1\setminus \bar{B_0}$ vanishing on the boundary. It is shown that the associated functional $J(\Om)$ is minimal if and only if the balls are concentric. It is also shown that the first Dirichlet eigenvalue of the Laplacian on $\Om$ is maximal if and only if the balls are concentric.

Affiliated with

Also associated with

No associations

Rating

On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms 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 On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On two functionals connected to the Laplacian in a class of doubly connected domains in space-forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-257163