Form-perturbation theory for higher-order elliptic operators and systems by singular potentials

We give a form-perturbation theory by singular potentials for scalar elliptic operators onL2(Rd)of order 2mwith Holder continuous coefficients. The form-bounds are obtained from anL(1)functional analytic approach which takes advantage of both the existence ofm-gaussian kernel estimates and the holomorphy of the semigroup inL1(Rd).We also explore the (local) Kato class potentials in terms of (local) weak compactness properties. Finally, we extend the results to elliptic systems and singular matrix potentials. This article is part of the theme issue `Semigroup applications everywhere'.