J. Math. Pures Appl. 100 (2013) 535–563 www.elsevier.com/locate/matpur
Parabolic equations with p, q-growth Verena Bögelein a,∗ , Frank Duzaar a , Paolo Marcellini b a Department Mathematik, Universität Erlangen–Nürnberg, Cauerstrasse 11, 91058 Erlangen, Germany b Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
Received 21 February 2012 Available online 29 January 2013
Abstract We consider parabolic equations of the type ∂t u − div a(x, t, Du) = 0 on a parabolic space–time cylinder ΩT . The vector field a is assumed to satisfy a non-standard p, q-growth assumption. When 2pq
