2 00 3 The comparsion principle for viscosity solutions of fully nonlinear subelliptic equations in Carnot groups
نویسنده
چکیده
For any Carnot group G and a bounded domain Ω ⊂ G, we prove that viscosity solutions in C(Ω̄) of the fully nonlinear subelliptic equation F (u,∇hu,∇ 2 hu) = 0 are unique when F ∈ C(R×R×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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تاریخ انتشار 2003