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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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