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

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.

9 pages

References in corpus (1)

• Sharp exponents and a Wiener type condition for boundary regularity of quasiminimizers

Cited by in corpus (3)

• The Liouville theorem for $p$-harmonic functions and quasiminimizers with finite energy
• Poincaré inequalities and $A_p$ weights on bow-ties
• The quasisuperminimizing constant for the minimum of two quasisuperminimizers in R^n