A new class of p-Harmonic maps into sphere

A new class of p-Harmonic maps into sphere

In this paper we introduce a class of maps referred to as generalised twists and examine them in connection with the Euler-Lagrange equations associated with Fp over Ap(Ω). The main result is a surprising discrepancy between even and odd dimensions. Here we show that in even dimensions the latter system of equations admit innitely many smooth solutions, modulo isometries, amongst such maps. In odd dimensions this number reduces to one. The result relies on a careful analysis of the full versus the restricted Euler-Lagrange equations.