| Title:
|
An elementary proof of Marcellini Sbordone semicontinuity theorem (English) |
| Author:
|
Roskovec, Tomáš G. |
| Author:
|
Soudský, Filip |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
59 |
| Issue:
|
5 |
| Year:
|
2023 |
| Pages:
|
723-736 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The weak lower semicontinuity of the functional $$ F(u)=\int_{\Omega}f(x,u,\nabla u) {\rm d} x $$ 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 $W^{1,p}(\Omega)$. 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. (English) |
| Keyword:
|
convexity |
| Keyword:
|
sequential semicontinuity |
| Keyword:
|
calculus of variation |
| Keyword:
|
minimizer |
| MSC:
|
46E35 |
| MSC:
|
49J20 |
| MSC:
|
49J45 |
| idZBL:
|
Zbl 07790658 |
| idMR:
|
MR4681019 |
| DOI:
|
10.14736/kyb-2023-5-0723 |
| . |
| Date available:
|
2023-12-12T15:59:32Z |
| Last updated:
|
2024-02-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151984 |
| . |
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