| bibtype |
J -
Journal Article
|
| ARLID |
0646631 |
| utime |
20260226111637.3 |
| mtime |
20260226235959.9 |
| SCOPUS |
105030300067 |
| DOI |
10.1007/s00526-026-03262-z |
| title
(primary) (eng) |
Polyconvex double well functions |
| specification |
| page_count |
10 s. |
| media_type |
P |
|
| serial |
| ARLID |
cav_un_epca*0252329 |
| ISSN |
0944-2669 |
| title
|
Calculus of Variations and Partial Differential Equations |
| volume_id |
65 |
| publisher |
|
|
| keyword |
polyconvexity |
| keyword |
double well |
| keyword |
integral function |
| author
(primary) |
| ARLID |
cav_un_auth*0015534 |
| name1 |
Henrion |
| name2 |
D. |
| country |
FR |
|
| author
|
| ARLID |
cav_un_auth*0101142 |
| name1 |
Kružík |
| name2 |
Martin |
| institution |
UTIA-B |
| full_dept (cz) |
Matematická teorie rozhodování |
| full_dept |
Department of Decision Making Theory |
| department (cz) |
MTR |
| department |
MTR |
| share |
50 |
| garant |
K |
| fullinstit |
Ústav teorie informace a automatizace AV ČR, v. v. i. |
|
| source |
|
| source |
|
| cas_special |
| project |
| project_id |
GA24-10366S |
| agency |
GA ČR |
| country |
CZ |
| ARLID |
cav_un_auth*0472839 |
|
| abstract
(eng) |
We investigate polyconvexity of the double well function f(X):=|X-X1|2|X-X2|2 for given matrices X1,X2∈Rn×n. Such functions are fundamental in the modeling of phase transitions in materials, but their non-convex nature presents challenges for the analysis of variational problems. Polyconvexity of f is related to the singular values of the matrix difference X1-X2. We prove that f is polyconvex if and only if the square of the largest singular value does not exceed the sum of the squares of the other singular values. This condition allows the function to be decomposed into the sum of a strictly convex part and a null Lagrangean. As a direct application of this result, we prove an existence and uniqueness theorem for the corresponding Dirichlet minimization problem of the integral functional. |
| reportyear |
2027 |
| RIV |
BA |
| result_subspec |
WOS |
| FORD0 |
10000 |
| FORD1 |
10100 |
| FORD2 |
10102 |
| num_of_auth |
2 |
| inst_support |
RVO:67985556 |
| permalink |
https://hdl.handle.net/11104/0376330 |
| confidential |
S |
| article_num |
88 |
| mrcbC91 |
A |
| mrcbT16-e |
MATHEMATICS.APPLIED|MATHEMATICS |
| mrcbT16-f |
2.4 |
| mrcbT16-g |
0.5 |
| mrcbT16-h |
7.4 |
| mrcbT16-i |
0.01644 |
| mrcbT16-j |
1.845 |
| mrcbT16-k |
6551 |
| mrcbT16-q |
87 |
| mrcbT16-s |
2.405 |
| mrcbT16-y |
35.34 |
| mrcbT16-x |
1.98 |
| mrcbT16-3 |
1550 |
| mrcbT16-4 |
Q1 |
| mrcbT16-5 |
1.900 |
| mrcbT16-6 |
245 |
| mrcbT16-7 |
Q1 |
| mrcbT16-C |
87.2 |
| mrcbT16-M |
1.48 |
| mrcbT16-N |
Q1 |
| mrcbT16-P |
93 |
| arlyear |
2026 |
| mrcbU14 |
105030300067 SCOPUS |
| mrcbU24 |
PUBMED |
| mrcbU34 |
WOS |
| mrcbU63 |
cav_un_epca*0252329 Calculus of Variations and Partial Differential Equations Roč. 65 č. 3 2026 0944-2669 1432-0835 Springer |
|