Tensor products and sums of p-harmonic functions, quasiminimizers and p-admissible weights

TL;DR

This paper investigates how tensor products and sums of p-harmonic functions and quasiminimizers behave, showing they preserve quasiminimizer properties in weighted and metric spaces, extending understanding of these functions.

Contribution

It demonstrates that tensor products and sums of quasiminimizers remain quasiminimizers in weighted and metric spaces, extending previous results on p-harmonic functions.

Findings

Tensor product of two p-harmonic functions is a quasiminimizer.

Tensor product of two quasiminimizers is a quasiminimizer.

Tensor product of p-admissible measures remains p-admissible.

Abstract

The tensor product of two p-harmonic functions is in general not p-harmonic, but we show that it is a quasiminimizer. More generally, we show that the tensor product of two quasiminimizers is a quasiminimizer. Similar results are also obtained for quasisuperminimizers and for tensor sums. This is done in weighted R^n with p-admissible weights. It is also shown that the tensor product of two p-admissible measures is p-admissible. This last result is generalized to metric spaces.