Notes on Optimal Flux Fields

TL;DR

This paper investigates the optimal flux fields within a region under specified boundary conditions, optimizing certain norms and analyzing the region's capacity to handle various fluxes and densities.

Contribution

It introduces a framework for determining optimal flux fields based on $L^{p}$ and Sobolev-like norms, and analyzes the capacity of regions to accommodate different boundary fluxes.

Findings

Optimal flux fields can be characterized by specific norm minimizations.

The capacity of a region to handle flux variations is quantitatively analyzed.

The approach provides insights into flux distribution optimization under boundary constraints.

Abstract

For a given region, and specified boundary flux and density rate of an extensive property, the optimal flux field that satisfies the balance conditions is considered. The optimization criteria are the $L^{p}$-norm and a Sobolev-like norm of the flux field. Finally, the capacity of the region to accommodate various boundary fluxes and density rates is defined and analyzed.