Parabolic equations with p,qp,q-growth

We consider parabolic equations of the type∂tu−diva(x,t,Du)=0∂tu−diva(x,t,Du)=0 on a parabolic space–time cylinder ΩTΩT. The vector field a   is assumed to satisfy a non-standard p,qp,q-growth assumption. When2⩽p⩽q

RésuméOn considère lʼéquation parabolique∂tu−diva(x,t,Du)=0∂tu−diva(x,t,Du)=0 sur le cylindre parabolique espace–temps ΩTΩT. Le champ vectoriel a satisfait les conditions non standard de croissance p, q. Lorsque2⩽p⩽q