Lower semicontinuity in BV of quasiconvex integrals with subquadratic growth
Revised: 2 March 2012
A lower semicontinuity result in BV is obtained for quasiconvex integrals with subquadratic growth. The key steps in this proof involve obtaining boundedness properties for an extension operator, and a precise blow-up technique that uses fine properties of Sobolev maps. A similar result is obtained by Kristensen in [Calc. Var. Partial Differ. Equ. 7 (1998) 249–261], where there are weaker asssumptions on convergence but the integral needs to satisfy a stronger growth condition.
Mathematics Subject Classification: 49J45
Key words: Lower semicontinuity / quasiconvex integrals / functions of bounded variation
© EDP Sciences, SMAI, 2013