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An open-loop two-person zero-sum linear quadratic (LQ for short) stochastic differential game is considered. The controls for both players are allowed to appear in both the drift and diffusion of the state equation, the weight-ing matrices in the payoff/cost functional are not assumed to be definite/non-singular, and the cross-terms between two controls are… (More)

Here we obtain everywhere regularity of weak solutions of some nonlinear elliptic systems with borderline growth, including n-harmonic maps between manifolds or map with constant volumes. Other results in this paper include regularity up to the boundary and a removability theorem for isolated singularities. is the set of all functions u ∈ L p (Ω, R m) with… (More)

- Michael McAsey, Libin Mou
- 2000

The mass transport problem seeks to find a transport plan to move mass distributed according to one measure and place it according to the distribution of a second measure so as to minimize total transportation costs. In many cases the first measure is known but the second is only partially specified. In such a case, part of the problem is to find the… (More)

- Libin Mou, Jiongmin Yong
- 2007

For a controlled stochastic differential equation with a Bolza type performance functional, a variational formula for the functional in a given control process direction is derived, by means of backward stochastic differential equations. As applications, some Pontryagin type maximum principles are established for optimal controls of control problems, for… (More)

- LIBIN H. MOU
- 1991

Here for a smooth bounded Euclidean domain Ω and a smooth Riemannian manifold N , we show that almost every smooth map ϕ : ∂Ω → N serves as boundary data for at most one energy minimizing map u : Ω → N [Theorem 5.2]. We also obtain some uniform boundary regularity estimates for energy minimizers [Theorem 2.1], which not only are important to our proof, but… (More)

- Michael McAsey, Libin Mou
- 2006

We study a class of rational matrix differential equations that generalize the Riccati differential equations. The generalization involves replacing positive definite " weighting " matrices in the usual Riccati equations with either semidefinite or indefinite matrices that arise in linear quadratic control problems and differential games−both stochastic and… (More)

- Michael McAsey, Libin Mou, Richard M. Aron
- 2007

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Abstract A multiplier rule is proved for constrained minimization problems defined on… (More)

- Libin Mou
- 2001

We use upper and lower solutions to study the existence and properties of solutions to differential Riccati equations arising from stochastic linear quadratic regulator (LQR) problems. The main results include an interpretation of upper and lower solutions, comparison theorems, an upper-lower solution theorem, necessary and sufficient conditions for… (More)

- Libin Mou
- 2001

The authors and colleagues, in work to be submitted for publication, have applied the method of upper and lower solutions to the study of Riccati equations of various types, including those in [1] [2] [3] [4] and [5]. In this note, we show how to estimate the maximal existence interval of the solution to the classical Riccati differential equation.

- Michael McAsey, Libin Mou
- 2001

In this paper we study a class of matrix differential and algebraic Riccati equations arising from stochastic differential games with a quadratic cost. We will use the notion of upper and lower solutions to give necessary and sufficient conditions for the existence of solutions to the equations. We also obtain a monotonicity, a comparison theorem and… (More)