The comparsion principle for viscosity solutions of fully nonlinear subelliptic equations in Carnot groups

Details The comparsion principle for viscosity solutions of fully nonlinear subelliptic equations in Carnot groups The comparsion principle for viscosity solutions of fully nonlinear subelliptic equations in Carnot groups

2003-09-04

arxiv.org/abs/math/0309078v1

Mathematics

Analysis of PDEs

15 pages

Scientific paper

For any Carnot group $\bf G$ and a bounded domain $\Omega\subset \bf G$, we prove that viscosity solutions in $C(\bar\Om)$ of the fully nonlinear subelliptic equation $F(u,\nabla_h u, \nabla^2_h u)=0$ are unique when $F\in C(R\times R^m\times {\Cal S}(m))$ satisfies (i) $F$ is degenerate subelliptic and decreasing in $u$ or (ii) $F$ is uniformly subelliptic and nonincreasing in $u$. This extends Jensen's uniqueness theorem from the Euclidean space to the sub-Riemannian setting of the Carnot group.

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