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A nonautonomous chain rule in W 1,p and BV |
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| Authors: | Luigi Ambrosio Graziano Crasta Virginia De Cicco Guido De Philippis |
| Institution: | 1. Scuola Normale Superiore, p.za dei Cavalieri 7, 56126, Pisa, Italy 2. Dipartimento di Matematica G. Castelnuovo, Università di Roma La Sapienza, P.le A. Moro 2, 00185, Rome, Italy 3. Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Università di Roma La Sapienza, Via A. Scarpa 10, 00185, Roma, Italy |
| Abstract: | In this paper we consider the chain rule formula for compositions ${x\mapsto F(x, u(x))}$ 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 C 1 with respect to z. Our results extend to this “nonautonomous” case the results known for compositions ${x\mapsto F(u(x))}$ . |
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