Nittka’s invariance criterion and Hilbert space valued parabolic equations in Lp

Abstract

Nittka gave an efficient criterion on a form defined on L2(Ω) which implies that the associated semigroup is Lp -invariant for some given p∈ (1 , ∞) . We extend this criterion to the Hilbert space valued L2(Ω , H) . As an application, we consider elliptic systems of purely second order. Our main result shows that the induced semigroup is Lp -contractive for all p∈ [p-, p+] for some 1 < p-< 2 < p+< ∞ .