  In two dimensions every weak solution to a nonlinear elliptic system
$\rm{div} a(x,u,Du)=0$ has H\"older continuous first derivatives provided that
standard continuity, ellipticity and growth assumptions hold with a growth
exponent $p \geq 2$. We give an example showing that this result cannot be
extended to the subquadratic case, i.e. that weak solutions are not necessarily
continuous if $1< p <2$. Furthermore, we discuss related results for
variational integrals.

Analysis of PDEs