A nonautonomous chain rule in W1,p and BV

Luigi Ambrosio; Graziano Crasta; Virginia de Cicco; Guido de Philippis

doi:10.1007/s00229-012-0548-z

A nonautonomous chain rule in W^1,p and BV

Luigi Ambrosio, Graziano Crasta, Virginia de Cicco, Guido de Philippis

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we consider the chain rule formula for compositions x {mapping} 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 {mapping} F(u(x)).

Original language	English (US)
Pages (from-to)	461-480
Number of pages	20
Journal	manuscripta mathematica
Volume	140
Issue number	3-4
DOIs	https://doi.org/10.1007/s00229-012-0548-z
State	Published - Mar 2013

ASJC Scopus subject areas

General Mathematics

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Cite this

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abstract = "In this paper we consider the chain rule formula for compositions x {mapping} 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 {mapping} F(u(x)).",

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AU - Crasta, Graziano

AU - de Cicco, Virginia

AU - de Philippis, Guido

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N2 - In this paper we consider the chain rule formula for compositions x {mapping} 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 {mapping} F(u(x)).

AB - In this paper we consider the chain rule formula for compositions x {mapping} 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 {mapping} F(u(x)).

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A nonautonomous chain rule in W^1,p and BV

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