Generalized Spectrum of Second Order Differential Operators
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F20%3A00532921" target="_blank" >RIV/67985807:_____/20:00532921 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/20:10422198
Result on the web
<a href="http://dx.doi.org/10.1137/20M1316159" target="_blank" >http://dx.doi.org/10.1137/20M1316159</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/20M1316159" target="_blank" >10.1137/20M1316159</a>
Alternative languages
Result language
angličtina
Original language name
Generalized Spectrum of Second Order Differential Operators
Original language description
We analyze the spectrum of the operator Delta(-1)[Delta . (K del u)], where Delta denotes the Laplacian and K = K(x, y) is a symmetric tensor. Our main result shows that this spectrum can be derived from the spectral decomposition K = Q Lambda Q(T), where Q = Q(x, y) is an orthogonal matrix and Lambda = Lambda(x, y) is a diagonal matrix. More precisely, provided that K is continuous, the spectrum equals the convex hull of the ranges of the diagonal function entries of A. The involved domain is assumed to be bounded and Lipschitz, and both homogeneous Dirichlet and homogeneous Neumann boundary conditions are considered. We study operators defined on infinite dimensional Sobolev spaces. Our theoretical investigations are illuminated by numerical experiments, using discretized problems. The results presented in this paper extend previous analyses which have addressed elliptic differential operators with scalar coefficient functions. Our investigation is motivated by both preconditioning issues (efficient numerical computations) and the need to further develop the spectral theory of second order PDEs (core analysis).
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
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GC17-04150J" target="_blank" >GC17-04150J: Reliable two-scale Fourier/finite element-based simulations: Error-control, model reduction, and stochastics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Numerical Analysis
ISSN
0036-1429
e-ISSN
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Volume of the periodical
58
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
2193-2211
UT code for WoS article
000568220000008
EID of the result in the Scopus database
2-s2.0-85091816867