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Abstract
We study weak lower semicontinuity of integral functionals in W1,p under standard p-growth conditions, with integrands whose negative part may have p-growth as well. A characterization is obtained which, besides quasiconvexity of the integrand, involves a second condition that in general is weaker than boundary quasiconvexity at zero as defined by Ball and Marsden, although for p-homogeneous integrands, it reduces to the latter.
Keywords.: Weak lower semicontinuity; lower bound; multiple integrals; quasiconvexity at the boundary
Received: 2009-11-19
Revised: 2010-03-12
Accepted: 2010-03-17
Published Online: 2010-07-20
Published in Print: 2010-October
© de Gruyter 2010
