The paper is concerned with an application of a new chain rule formula to the lower semicontinuity in $W^{1,1}$ of integral functionals of this type $$F(u)=\int_{\Omega}f(x,u(x),\nabla u(x))dx.$$ A sufficient condition for lower semicontinuity is given. Essentially, the assumption of weak differentiability of f in x is replaced with a BV dependence on x.
A chain rule formula in $BV$ and application to lower semicontinuity / V., DE CICCO; Fusco, Nicola; Verde, Anna. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 28:4(2007), pp. 427-447. [10.1007/s00526-006-0048-7]
A chain rule formula in $BV$ and application to lower semicontinuity
FUSCO, NICOLA;VERDE, ANNA
2007
Abstract
The paper is concerned with an application of a new chain rule formula to the lower semicontinuity in $W^{1,1}$ of integral functionals of this type $$F(u)=\int_{\Omega}f(x,u(x),\nabla u(x))dx.$$ A sufficient condition for lower semicontinuity is given. Essentially, the assumption of weak differentiability of f in x is replaced with a BV dependence on x.| File | Dimensione | Formato | |
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