Calculus of Variations and Geometric Measure Theory

D. Di Donato

Intrinsic Lipschitz maps vs. Lagrangian type solutions in Carnot groups of step 2

created by didonato on 01 Sep 2021



Inserted: 1 sep 2021

Year: 2021

ArXiv: 2108.02298 PDF


We focus our attention on the notion of intrinsic Lipschitz graphs, inside a subclass of Carnot groups of step 2 which includes a corank 1 Carnot groups (and so the Heisenberg groups), Free groups of step 2 and the complexified Heisenberg group. More precisely, we prove the equivalence between intrinsic Lipschitz map and a weak solution to a suitable non linear first order PDE system, which generalizes Lagrangian solution in the context of Heisenberg groups.