Showing papers by "Paris Dauphine University published in 1987"

Solutions of Hartree-Fock equations for Coulomb systems

Abstract: This paper deals with the existence of multiple solutions of Hartree-Fock equations for Coulomb systems and related equations such as the Thomas-Fermi-Dirac-Von Weizacker equation.

Subharmonics for convex nonautonomous Hamiltonian systems

Abstract: On etudie des solutions periodiques du systeme hamiltonien −Jx˙=H'(t,x) ou J est la matrice symplectique standard et H∈C 2 (R×R 2n ,R) est T-periodique en la premiere variable pour tout (t,x). H'(t,x) note le gradient partiel par rapport a la seconde variable

An approximation method for stochastic control problems with partial observation of the state — a method for constructing ∈-optimal controls

Abstract: We consider a continuous-time stochastic control problem with partial observations. Given some assumptions, we reduce the problem in successive approximation steps to a discrete-time, complete-observation, stochastic control problem with a finite number of possible states and controls. For the latter problem an optimal control can always be explicitly computed. Convergence of the approximations is shown, which in turn implies that an optimal control for the last-stage approximating problem is ∈-optimal for the original problem.

Global and Local Invariants for Convex Energy Surfaces and their Periodic Trajectories: A Survey

Abstract: Denote by the usual Inner product in R 2n and let J be the standard complex structure on R 2n given by the matrix $$ J = \left[ {\begin{array}{*{20}{c}} {{0_n}} { = {1_n}} \\ {{1_n}} {{0_n}} \\ \end{array} } \right] $$ Associated to J and is the canonical 2-form Ω defined by $$ \Omega = \left\langle {J \cdot, \cdot } \right\rangle $$

Recent Progress on First Order Hamilton-Jacobi Equations

Abstract: Publisher Summary This chapter discusses recent progress on first order Hamilton-Jacobi equations (HJ). It explains viscosity solutions and their uniqueness. The continuous function obtained by the vanishing viscosity method is viscosity solutions. The chapter concentrates on existence and uniquesness questions, ideas and results for which are taken from studies conducted by various authors. A complete self-contained treatment of HJ via viscosity solutions is given. HJ are nonlinear first-order equations, which were first introduced in the context of the calculus of variations. The chapter describes that the uniqueness part also yields a priori estimates: bounds or local bounds, moduli of uniform continuity.

Discretization of the Bellman equation and the corresponding stochastic control problem

Abstract: IXTRODUCTIOF u (x ) = I n f J x ( z ( . ) ) ( 1 . 1 1 ) Z(.) We review some o f t h e c u r r e n t d i s c r e t i z a t i o n s c h e mes u s e d i n t h e c o t e x t of Bellman equations. Our main 1 . 2 . S o t a t i o n f r d i s c r e t i z a t i o n o b j e c t i v e i s t o t r e a t c a s e s when the Hami l tonian has Le t h be a small parameter such tha t h = 1 / R , X quadra t ic g rowth and we s h a l l compare wi th the more c las in teger t ending to + * We consider the grid O f size s i c a l s i t u a t i o n when the Hami l tonian has l inear g rowth . h , i * e * the Points 2% Y j = O , * . * >s* We s h a l l d i s c u s s t h e a s s o c i a t e d s t o c h a s t i c o n t r o l p r o Let blem i n d i s c r e t e t i m e when t h e r e i s one. The a n a l y t i c H = s e t of s t e p f u n c t i o n s w h i c h a r e c o n s t a n t on par t of t h e p a p e r r e l i e s on r e s u l t s of R. GLOWINSKI and t h e A. h i n t e r v a l s ( j h , ( j + l ) h ) , j = O ,... ,5-1.

Viterbo’s Proof of Weinstein’s Conjecture in R2n

Abstract: This is a sketch of Viterbo’s recent proof of the Weinstein conjecture: a hypersurface of contact type in R 2n carries at least one closed trajectory.