Oscillations and concentrations in sequences of gradients

0086858 - ÚTIA 2008 RIV FR eng J - Journal Article
Kalamajska, A. - Kružík, Martin
Oscillations and concentrations in sequences of gradients.
[Oscilace a koncentrace v posloupnostech gradientu.]
ESAIM-Control Optimisation and Calculus of Variations. Roč. 14, č. 1 (2008), s. 71-104. ISSN 1292-8119. E-ISSN 1262-3377
R&D Projects: GA AV ČR IAA1075402
Institutional research plan: CEZ:AV0Z1075907
Keywords : oscillations * concentrations
Subject RIV: BA - General Mathematics
Impact factor: 0.787, year: 2008

We use DiPerna's and Majda's generalization of Young measures to describe oscillations and concentrations in sequences of gradients bounded in Lebesgue spaces. Our main result is a characterization of those DiPerna-Majda measures which are generated by gradients of Sobolev maps satisfying the same fixed Dirichlet boundary condition. Cases where no boundary conditions nor regularity of the domain are required and links with lower semicontinuity results by Meyers and by Acerbi and Fusco are also discussed.

Charakterizujeme oscilace a koncentrace v posloupnostech gradientu sobolevskych funkci s pouzitim tzv. DiPernovych-Majdovych mer. Explicitni charakterizace je je dana v pripade, kdy cleny posloupnosti maji stejne stopy. Dusledkem teto charakterizace jsou vety o slabe zdola polospojitosti integralnich funkcionalu.
Permanent Link: http://hdl.handle.net/11104/0149007