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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

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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.