A SUB-RIEMANNIAN MAXIMUM PRINCIPLE AND ITS APPLICATION TO THE p-LAPLACIAN IN CARNOT GROUPS

作者：Bieske Thomas^*

来源：Annales Academiae Scientiarum Fennicae-Mathematica, 2012, 37(1): 119-134.

DOI：10.5186/aasfm.2012.3706

• Sub-Riemannian geometry
• non-linear potential theory
• viscosity solutions
• p-Laplacian

We prove a sub-Riemannian maximum principle for semicontinuous functions. We apply this principle to Carnot groups to provide a %26quot;sub-Riemannian%26quot; proof of the uniqueness of viscosity infinite harmonic functions. This is an alternate method of proof from the one found in [15]. We also establish the equivalence of weak solutions and viscosity solutions to the p-Laplace equation. This result extends the author%26apos;s previous work in the Heisenberg group [3, 4].

• 出版日期2012