In this paper we consider the chain rule formula for compositions x bar right arrow F(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 C (1) with respect to z. Our results extend to this "nonautonomous" case the results known for compositions x bar right arrow F(u(x)).
A nonautonomous chain rule in W-1,W-p and BV / Luigi, Ambrosio; Crasta, Graziano; DE CICCO, Virginia; Guido De, Philippis. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - STAMPA. - 140:3-4(2013), pp. 461-480. [10.1007/s00229-012-0548-z]
A nonautonomous chain rule in W-1,W-p and BV
CRASTA, Graziano;DE CICCO, Virginia;
2013
Abstract
In this paper we consider the chain rule formula for compositions x bar right arrow F(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 C (1) with respect to z. Our results extend to this "nonautonomous" case the results known for compositions x bar right arrow F(u(x)).File allegati a questo prodotto
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