## Optimal regularity for quasilinear equations in stratified nilpotent Lie groups and applications.(English)Zbl 0870.35019

Summary: 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 $$H^{n}$$.

### MSC:

 35B65 Smoothness and regularity of solutions to PDEs 35J70 Degenerate elliptic equations
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### References:

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