We consider a functional of the type F(u) = integral F-Omega(x,u, ..., D(k)u) dx, where Omega is an open bounded set of R-n and F is a Caratheodory function. By an approximation argument we prove the lower semincontinuity of F with respect to the weak topology of W-k,W-p(Omega; R-m) under p-growth conditions for the integrand F.
Lower semicontinuity for quasiconvex integrals of higher order / L. POGGIOLINI; M. GUIDORZI. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - STAMPA. - 6 no. 2:(1999), pp. 227-246. [10.1007/s000300050074]
Lower semicontinuity for quasiconvex integrals of higher order
POGGIOLINI, LAURA;
1999
Abstract
We consider a functional of the type F(u) = integral F-Omega(x,u, ..., D(k)u) dx, where Omega is an open bounded set of R-n and F is a Caratheodory function. By an approximation argument we prove the lower semincontinuity of F with respect to the weak topology of W-k,W-p(Omega; R-m) under p-growth conditions for the integrand F.
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