Energy integrals and asymmetric co-potentials for closed forms

Abstract

We investigate the class of measures of finite energy integrals and the behavior of potentials and co-potentials associated with non-symmetric closed forms. In particular, we compare these objects with their symmetric counterparts from three viewpoints: a non-symmetric version of Stollmann--Voigt's inequality, non-symmetric perturbations of symmetric forms, and closed forms associated with non-symmetric jump-type forms. Our results indicate that measures of finite energy integrals, potentials, and co-potentials behave differently in the non-symmetric setting, requiring more delicate analysis than in the symmetric case.