An elementary proof of Marcellini Sbordone semicontinuity theorem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F23%3A00012106" target="_blank" >RIV/46747885:24510/23:00012106 - isvavai.cz</a>
Alternative codes found
RIV/60076658:12410/23:43906883
Result on the web
<a href="https://www.kybernetika.cz/content/2023/5/723" target="_blank" >https://www.kybernetika.cz/content/2023/5/723</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14736/kyb-2023-5-0723" target="_blank" >10.14736/kyb-2023-5-0723</a>

Result language
angličtina
Original language name
An elementary proof of Marcellini Sbordone semicontinuity theorem
Original language description
The weak lower semicontinuity of the functional F(u) = f (x, u, backward difference u) dx omega is a classical topic that was studied thoroughly. It was shown that if the function f is continuous and convex in the last variable, the functional is sequentially weakly lower semicontinuous on W1,P(omega). However, the known proofs use advanced instruments of real and functional analysis. Our aim here is to present a proof understandable even for students familiar only with the elementary measure theory.
Czech name
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Czech description
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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
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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