Extremal first Dirichlet eigenvalue of doubly connected plane domains and dihedral symmetry

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dc.creatorSoufi, Ahmad El
dc.creatorKiwan, Rola
dc.date2007-05-09
dc.date.accessioned2026-07-07T08:47:44Z
dc.date.available2026-07-07T08:47:44Z
dc.descriptionWe deal with the following eigenvalue optimization problem: Given a bounded domain $D\subset \R^2$, how to place an obstacle $B$ of fixed shape within $D$ so as to maximize or minimize the fundamental eigenvalue $λ_1$ of the Dirichlet Laplacian on $D\setminus B$. This means that we want to extremize the function $ρ\mapsto λ_1(D\setminus ρ(B))$, where $ρ$ runs over the set of rigid motions such that $ρ(B)\subset D$. We answer this problem in the case where both $D$ and $B$ are invariant under the action of a dihedral group $\mathbb{D}_n$, $n\ge2$, and where the distance from the origin to the boundary is monotonous as a function of the argument between two axes of symmetry. The extremal configurations correspond to the cases where the axes of symmetry of $B$ coincide with those of $D$.
dc.descriptionTo appear in SIAM Journal on Mathematical Analysis
dc.identifierhttps://arxiv.org/abs/0705.1262
dc.identifierhttp://arxiv.org/abs/0705.1262
dc.identifierSIAM Journal on Mathematical Analysis / SIAM Journal of Mathematical Analysis 39, 4 (2007) 1112 --1119
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/143704
dc.subjectSpectral Theory
dc.subjectOptimization and Control
dc.subject35J10, 35P15, 49R50, 58J50
dc.titleExtremal first Dirichlet eigenvalue of doubly connected plane domains and dihedral symmetry
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