## Archival Version

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://www.math.psu.edu/era/.
**

Optimal regularity for
quasilinear equations in stratified nilpotent
Lie groups and applications
**This journal is archived by the American Mathematical
Society. The master copy is available at
http://www.ams.org/era/
**

## Optimal regularity for
quasilinear equations in stratified nilpotent
Lie groups and applications

### Luca Capogna

**Abstract.**
We announce the optimal
$C^{1+\a}$ regularity of the gradient
of weak solutions to a class of quasilinear degenerate elliptic equations
in nilpotent stratified Lie groups of step two.
As a consequence we also prove a Liouville type theorem for
$1-$quasiconformal mappings between domains of the Heisenberg group
$\bh^n$.

*Copyright American Mathematical Society 1996*

**Retrieve entire article **

#### Article Info

- ERA Amer. Math. Soc.
**02** (1996), pp. 60-68
- Publisher Identifier: S 1079-6762(96)00009-6
- 1991
*Mathematics Subject Classification*. Primary 35H05
- Received by the editors March 15, 1996
- Communicated by Thomas Wolff
- Comments (When Available)

**Luca Capogna**

Department of Mathematics,
Purdue University,
West Lafayette, IN 47907

*E-mail address:* `capogna@math.purdue.edu`

Alfred P. Sloan Doctoral Dissertation Fellow.

*Electronic Research Announcements of the AMS *Home page