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

Abstract

We give a form-perturbation theory by singular potentials for scalar elliptic operators on [Formula: see text] of order 2m with Hölder continuous coefficients. The form-bounds are obtained from an L1 functional analytic approach which takes advantage of both the existence of m-gaussian kernel estimates and the holomorphy of the semigroup in [Formula: see text] 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'.