In this paper we consider the chain rule formula for compositions x↦F(x,u(x)) in the case when u has a Sobolev or BV regularity and F(x,z) is separately Sobolev, or BV, with respect to x and C1 with respect to z. Our results extend to this "nonautonomous" case the results known for compositions x↦F(u(x)).
A nonautonomous chain rule in W^{1,p} and BV
De Philippis, Guido
2013-01-01
Abstract
In this paper we consider the chain rule formula for compositions x↦F(x,u(x)) in the case when u has a Sobolev or BV regularity and F(x,z) is separately Sobolev, or BV, with respect to x and C1 with respect to z. Our results extend to this "nonautonomous" case the results known for compositions x↦F(u(x)).File in questo prodotto:
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2013_A non autonomous chain rule in $W^{1,p}$ and $BV$.pdf
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