REMARKS ON W-1,W-P-STABILITY OF THE CONFORMAL SET IN HIGHER DIMENSIONS

In this paper, we study the stability of maps in W-1,W-p that are clos e to the conformal set K-1 = R(+). SO(n) in an averaged sense as descr ibed in Definition 1.1. We prove that K-1 is W-1,W-p-compact for all p greater than or equal to n but is not W-1,W-p-stable for any 1 less t han or equal to p < n/2 when n greater than or equal to 3. We also pro ve a coercivity estimate for the integral functional integral(Rn) d(K1 )(p)(del phi(x)) dx on W-1,W-p(R(n);R(n)) for certain values of p lowe r than n using some new estimates for weak solutions of p-harmonic equ ations.