Sequential weak continuity of null Lagrangians at the boundary
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F14%3A00216040" target="_blank" >RIV/68407700:21110/14:00216040 - isvavai.cz</a>
Alternative codes found
RIV/67985556:_____/14:00392445
Result on the web
<a href="http://dx.doi.org/10.1007/s00526-013-0621-9" target="_blank" >http://dx.doi.org/10.1007/s00526-013-0621-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00526-013-0621-9" target="_blank" >10.1007/s00526-013-0621-9</a>
Alternative languages
Result language
angličtina
Original language name
Sequential weak continuity of null Lagrangians at the boundary
Original language description
We show weak* in measures on / weak-L1 sequential continuity of u -> f (x,delu) : W1,p(;Rm) -> L1(), where f (x, .) is a null Lagrangian for x element , it is a null Lagrangian at the boundary for x element and | f (x, A)| <= C(1 + |A|p). We also give aprecise characterization of null Lagrangians at the boundary in arbitrary dimensions. Our results explain, for instance, why u -> det delu : W1,n(;Rn) -> L1() fails to be weakly continuous. Further,we state a newweak lower semicontinuity theorem for integrands depending on null Lagrangians at the boundary. The paper closes with an example indicating that a well-known result on higher integrability of determinant by Müller (Bull. Am. Math. Soc. New Ser. 21(2): 245?248, 1989 ) need not necessarily extendto our setting. The notion of quasiconvexity at the boundary due to J.M. Ball and J. Marsden is central to our analysis.
Czech name
—
Czech description
—
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—
Result continuities
Project
<a href="/en/project/GAP201%2F10%2F0357" target="_blank" >GAP201/10/0357: Modern mathematical and computational models for inelastic processes in solids</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Calculus of Variations and Partial Differential Equations
ISSN
0944-2669
e-ISSN
—
Volume of the periodical
49
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
16
Pages from-to
1263-1278
UT code for WoS article
000334679400018
EID of the result in the Scopus database
—