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- W1639755590 abstract "and H is a given Hamiltonian, at least continuous and nondecreasing in u. Our main examples are the vector fields that generate the homogeneous Carnot groups [4, 7], and in that case DXu and D 2 Xu are called, respectively, the horizontal gradient and the horizontal Hessian. A theory of fully nonlinear subelliptic equations was started recently by Bieske [5, 6] and Manfredi [17, 3], and Monge-Ampere equations of the form (0.1) with H = f(x) are listed among the main examples. For such equations on the Heisenberg group Gutierrez and Montanari [12] proved, among other things, a comparison principle among smooth suband supersolutions (see also [11] for related results). An example that motivates the dependence on the gradient DXu in H is the prescribed horizontal Gauss curvature equation in Carnot groups, as defined by Danielli, Garofalo and Nhieu [10]," @default.
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- W1639755590 date "2008-01-01" @default.
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- W1639755590 title "Comparison principles for subelliptic equations of Monge-Ampère type" @default.
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