SHAPES OF DRUMS WITH LOWEST BASE FREQUENCY UNDER NON-ISOTROPIC PERIMETER CONSTRAINTS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11620%2F19%3A10403972" target="_blank" >RIV/00216208:11620/19:10403972 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cbqEcc6Vd-" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cbqEcc6Vd-</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/tran/7532" target="_blank" >10.1090/tran/7532</a>

Jazyk výsledku

angličtina

Název v původním jazyce

SHAPES OF DRUMS WITH LOWEST BASE FREQUENCY UNDER NON-ISOTROPIC PERIMETER CONSTRAINTS

Popis výsledku v původním jazyce

We study the minimizers of the sum of the principal Dirichlet eigenvalue of the negative Laplacian and the perimeter with respect to a general norm in the class of Jordan domains in the plane. This is equivalent (modulo scaling) to minimizing the said eigenvalue (or the base frequency of a drum of this shape) subject to a hard constraint on the perimeter. We show that, for all norms, a minimizer exists, is unique up to spatial translations, and is convex but not necessarily smooth. We give conditions on the norm that characterize the appearance of facets and corners. We also demonstrate that near minimizers have to be close to the optimal ones in the Hausdorff distance. Our motivation for considering this class of variational problems comes from a study of random walks in random environment interacting through the boundary of their support.

Název v anglickém jazyce

SHAPES OF DRUMS WITH LOWEST BASE FREQUENCY UNDER NON-ISOTROPIC PERIMETER CONSTRAINTS

Popis výsledku anglicky

We study the minimizers of the sum of the principal Dirichlet eigenvalue of the negative Laplacian and the perimeter with respect to a general norm in the class of Jordan domains in the plane. This is equivalent (modulo scaling) to minimizing the said eigenvalue (or the base frequency of a drum of this shape) subject to a hard constraint on the perimeter. We show that, for all norms, a minimizer exists, is unique up to spatial translations, and is convex but not necessarily smooth. We give conditions on the norm that characterize the appearance of facets and corners. We also demonstrate that near minimizers have to be close to the optimal ones in the Hausdorff distance. Our motivation for considering this class of variational problems comes from a study of random walks in random environment interacting through the boundary of their support.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA16-15238S" target="_blank" >GA16-15238S: Kolektivní chování velkých stochastických systémů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Transactions of the American Mathematical Society

ISSN

0002-9947

e-ISSN

—

Svazek periodika

372

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

25

Strana od-do

71-95

Kód UT WoS článku

000472528700004

EID výsledku v databázi Scopus

2-s2.0-85070291375