Abstract
In this paper the author proves theorems on passage to the limit in nonlinear parabolic equations of the form , arising in the theory of optimal control of random processes of diffusion type. Under the assumptions that i) the functions and have bounded Sobolev derivatives in , ii) the and are convex downwards in , iii) the are uniformly bounded in some domain , iv) a.e. in , v) the coefficients of linear combinations of satisfy certain smoothness conditions, it is proved that on for all implies on . The second derivatives of the and with respect to are understood in the generalized sense (as measures), and the equations and are considered in the lattice of measures.Bibliography: 10 titles.
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