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


Author: Luca Capogna
Journal: Electron. Res. Announc. Amer. Math. Soc. 2 (1996), 60-68
MSC (1991): Primary 35H05
DOI: https://doi.org/10.1090/S1079-6762-96-00009-1
MathSciNet review: 1405970
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Abstract: We announce the optimal $C^{1+\alpha }$ 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 $\mathbb {H}^{n}$.


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Additional Information

Luca Capogna
Affiliation: Department of Mathematics, Purdue University, West Lafayette, IN 47907
Email: capogna@math.purdue.edu

DOI: https://doi.org/10.1090/S1079-6762-96-00009-1
Received by editor(s): March 15, 1996
Additional Notes: Alfred P. Sloan Doctoral Dissertation Fellow.
Communicated by: Thomas Wolff
Article copyright: © Copyright 1996 American Mathematical Society

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