Sequential weak continuity of null Lagrangians at the boundary

0392445 - ÚTIA 2015 RIV DE eng J - Journal Article
Kalamajska, A. - Kraemer, S. - Kružík, Martin
Sequential weak continuity of null Lagrangians at the boundary.
Calculus of Variations and Partial Differential Equations. Roč. 49, 3/4 (2014), s. 1263-1278. ISSN 0944-2669. E-ISSN 1432-0835
R&D Projects: GA ČR GAP201/10/0357
Institutional support: RVO:67985556
Keywords : null Lagrangians * nonhomogeneous nonlinear mappings * sequential weak/in measure continuity
Subject RIV: BA - General Mathematics
Impact factor: 1.518, year: 2014
http://library.utia.cas.cz/separaty/2013/MTR/kruzik-sequential weak continuity of null lagrangians at the boundary.pdf

We show sequential weak/in measure continuity of some nonhomogeneous nonlinear mappings. We also give a precise characterization of null Lagrangians at the boundary in arbitrary dimensions. Further, we state a new weak 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 extend to our setting. The notion of quasiconvexity at the boundary due to J.M. Ball and J. Marsden is central to our analysis.
Permanent Link: http://hdl.handle.net/11104/0221334