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

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/168441