A nonautonomous chain rule in W1,p and BV

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

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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 languageEnglish (US)
Pages (from-to)461-480
Number of pages20
Journalmanuscripta mathematica
Issue number3-4
StatePublished - 2013

ASJC Scopus subject areas

  • Mathematics(all)

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    Ambrosio, L., Crasta, G., de Cicco, V., & de Philippis, G. (2013). A nonautonomous chain rule in W1,p and BV. manuscripta mathematica, 140(3-4), 461-480. https://doi.org/10.1007/s00229-012-0548-z