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

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/115/01/0093-0102

• # Keywords

Eigenvalue problem; Laplacian; maximum principles

• # Abstract

LetB1 be a ball of radiusr1 inSn (ℍn), and letB0 be a smaller ball of radiusr0 such thatB0B1. ForSn we considerr1π. Let u be a solution of the problem- δm = 1 in Ω :=B1 /B0 vanishing on the boundary. It is shown that the associated functionalJ (Ω) is minimal if and only if the balls are concentric. It is also shown that the first Dirichlet eigenvalue of the Laplacian on Ω is maximal if and only if the balls are concentric.

• # Author Affiliations

1. Department of Mathematics, University of Mumbai, Mumbai - 400 098, India

• # Proceedings – Mathematical Sciences

Volume 132, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019