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Lower semicontinuity in BV of quasiconvex integrals with subquadratic growth

Published online by Cambridge University Press:  14 March 2013

Parth Soneji
Parth Soneji*
Affiliation:
Mathematical Institute, University of Oxford, 24-29 St Giles’ Oxford, OX1 3LB, UK. soneji@maths.ox.ac.uk; Parth.Soneji@maths.ox.ac.uk
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Abstract

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.

Keywords

Lower semicontinuityquasiconvex integralsfunctions of bounded variation
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 2 , April 2013 , pp. 555 - 573
Copyright
© EDP Sciences, SMAI, 2013

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