Weak convergence of minors

Using calculus of variations techniques, it is shown that if

converge to a function u in

,

where

RC="1998_05_19_733/fons-img3.gif">

is an open, bounded subset of ,

if the sequence of all minors

is equi-bounded in , and if

converge to a function f weakly in

, then

This result was previously obtained by Giaquinta, Modica and Soucek using

tools from Geometric Measure Theory, and it is sharp. In particular, for all

,

,

for all

SRC="1998_05_19_733/fons-img12.gif">,

and for every

This work in collaboration with Jan Malý was initiated during his visit to the

Max Planck Institute in March-April 1998.