To conclude this introduction we should also emphasise that while we have considered the more general case of generated prescribed Jacobian equations our results are also new for optimal transportation.
Using the estimates, (3.12) and (3.13), we can thus conclude from Theorem 1.1, the following global second derivative estimate for generated prescribed Jacobian equations.
The existence of locally smooth solutions to the second boundary value problem for generated prescribed Jacobian equations is treated in [16] under conditions A1, A2, A1*, A3 and A4w.
We shall establish the second derivative bounds for generated prescribed Jacobian equations under the hypotheses G1, G2, G1*, G3w and G4w introduced in [16], which extend the conditions A1, A2 and A3w for optimal transportation equations introduced in [20].
3, we will also discuss the application of Theorem 1.1 to global second derivative estimates for the Dirichlet and second boundary value problems for optimal transportation and generated prescribed Jacobian equations, yielding improvements of the corresponding results in [4, 13, 14, 20].
The matrix function A in the corresponding generated prescribed Jacobian equation is then given by A ( x, u, p ) = - Y p - 1 ( Y x + Y u ⊗ p ) = g x x [ x, Y, Z ], (1.2 where Y = Y ( x, u, p ) and Z = Z ( x, u, p ).
Initially, we explored using Medicaid pharmacy data to both generate prescribing profiles and to measure changes in behavior following our intervention.
This, once again, prevented us from generating the prescribed operating signals.
A constructive procedure for generating a prescribed unitary transform via the optically driven evolution of a multilevel atom is described.
Shear bands were generated under prescribed and controlled conditions in an AISI 304L stainless steel (Fe 18%Cr 8%Ni).
