ABSTRACT: Consider quasilinear elliptic equations of
-Laplacian type
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In the case of the Heisenberg group much less is known without any
additional hypothesis. It was shown by Capogna that the boundedness
of the horizontal gradient
implies the smoothness of
the solution
. In this talk we will show that when
is an
interval
the horizontal gradient
is
indeed locally bounded. Our proof is based on using a type of
unbalanced Moser iteration. We obtain the values
and
.
This is joint work with Giuseppe Mingione from the University of Parma.