SHAPES OF DRUMS WITH LOWEST BASE FREQUENCY UNDER NON-ISOTROPIC PERIMETER CONSTRAINTS
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
SHAPES OF DRUMS WITH LOWEST BASE FREQUENCY UNDER NON-ISOTROPIC PERIMETER CONSTRAINTS
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10103 - Statistics and probability
Result continuities
Project
<a href="/en/project/GA16-15238S" target="_blank" >GA16-15238S: Collective behavior of large stochastic systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Transactions of the American Mathematical Society
ISSN
0002-9947
e-ISSN
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Volume of the periodical
372
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
25
Pages from-to
71-95
UT code for WoS article
000472528700004
EID of the result in the Scopus database
2-s2.0-85070291375