Publication at Faculty of Mathematics and Physics |
2021
Abstract
For possibly discontinuous functions including, for instance, Sobolev functions, we present new Blaschke-Privaloff-type criteria for superharmonicity and harmonicity. This opens the way for introduction of a substantial generalization of the Laplace operator.
These potentialtheoretic considerations lead to a new kind of non-absolutely convergent integral where the integrand may be a highly oscillating pointwise function or even a distribution-valued function. In turn, this integral gives a precise meaning to some generalized Poisson equations with a wild right hand side.