We study the optimal control problem in coefficients for degenerate parabolic variational inequality. Since problems of this type may have Lavrent’ev effect, we consider a class so-called H-admissible solutions. substantiate attainability H-optimal pairs via solutions some nondegenerate perturbed under condition solvability original problem.

We investigate the optimal control problem with respect to coefficients of degenerate parabolic variational inequality. Since problems this type can have Lavrentieff effect, we consider in a class so-called Hadmissible solutions. substantiate attainability H-optimal pairs via solutions some nondegenerate perturbed problems.

Results concerning existence and characterization of optimal controls for ergodic control of nondegenerate diffusion processes are described. Extensions to the general ‘controlled martingale problem’ are indicated, which cover in particular degenerate diffusions and some infinite dimensional problems. In conclusion, some related problems and open issues are discussed. Mathematics Subject Classi...

We investigate the validity of the bootstrap method for the elementary symmetric polynomials S both xed and increasing order k, as n ! 1 the cases where = EX 1 6 = 0, the nondegenerate case, and where = EX 1 = 0, the degenerate case, are considered.

A new spectrum generating algebra for a unified description of rotations and vibrations in polyatomic molecules is introduced. An application to nonlinear X3 molecules shows that this model (i) incorporates exactly the relevant point group, (ii) provides a complete classification of oblate top states, and (iii) treats properly both degenerate and nondegenerate vibrations. PACS numbers: 33.20.-t...

This paper deals with global existence and uniqueness for the lake equations with a bottom topography vanishing on the shore. Our result generalizes previous studies that assumed the depth to be nondegenerate. Elliptic estimates for degenerate equations are established studying the behavior of the associated Green function.

We present an algorithm for computing the main topological characteristics of three-dimensional bodies. The algorithm is based on a dis-cretization of Morse theory and uses discrete analogs of smooth functions with only nondegenerate (Morse) and the simplest degenerate critical points.