ABSTRACT: Consider quasilinear elliptic equations of -Laplacian type
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.