(untitled) (European Journal of Pure and Applied Mathematics, 2025)
For a C^2-function f(x) on a bounded domain ω in R^2 the flux is defined by means of outer normal derivative of f. In this paper, we introduce the notion of flux(f) for any real-valued function on R^2. We define flux on bounded domain ω and take limits when ω grows into R^2 and the limit is defined as "at infinity", the flux(f) at infinity denoted as flux_∞ f. This limit flux_∞ f may or may not be finite. The related development is carried out by employing the notion of inversion on R^2 and the fact that a harmonic function defined outside a compact set in R^2 is the difference of two subharmonic functions on R^2 that are harmonic outside a compact set.