TITLE

New extremal domains for the first eigenvalue of the Laplacian in flat tori

AUTHOR(S)
Sicbaldi, Pieralberto
PUB. DATE
March 2010
SOURCE
Calculus of Variations & Partial Differential Equations;Mar2010, Vol. 37 Issue 3/4, p329
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We prove the existence of nontrivial compact extremal domains for the first eigenvalue of the Laplacian in manifolds $${\mathbb{R}^{n}\times \mathbb{R}{/}T\, \mathbb{Z}}$$ with flat metric, for some T > 0. These domains are close to the cylinder-type domain $${B_1 \times \mathbb{R}{/}T\, \mathbb{Z}}$$, where B1 is the unit ball in $${\mathbb{R}^{n}}$$, they are invariant by rotation with respect to the vertical axe, and are not invariant by vertical translations. Such domains can be extended by periodicity to nontrivial and noncompact domains in Euclidean spaces whose first eigenfunction of the Laplacian with 0 Dirichlet boundary condition has also constant Neumann data at the boundary.
ACCESSION #
47955915

 

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