Chinese Annals of Mathematics

In this paper, the authors study reiterated homogenization of nonlinear equations of the form -div(a(x,x/ε,x/ε²,Du_ε))=f, where a is periodic in the first two arguments and monotone in the third. It is proved that u_ε converges weakly in W^1,p(Ω) (and even in some multiscale sense), as ε→0 to the solution u₀ of a limit problem. Moreover, an explicit expression for the limit problem is given. The main results were also stated in [15]. This article presents the complete proofs of these results.

Under certain conditions, starting from the three-dimensional dynamic equations of elastic shells the author gives the justification of dynamic equations of flexural shells by means of the method of asymptotic analysis.

In a recent paper the author constructed a continuous map from the configuration space of n distinct ordered points in 3-space to the flag manifold of the unitary group U(n), which is compatible with the action of the symmetric group. This map is also compatible with appropriate actions of the rotation group SO(3). In this paper the author studies the induced homomorphism in SO(3)-equivariant cohomology and shows that this contains much interesting information involving representations of the symmetric group.

This paper is concerned with the boundedness of solutions for second order differential equations , which are neither dissipative nor conservative, and where the functions f and g are odd in x and even in t, which are 1-periodic in t, and the function g satisfies , as|x|→+∞. Using the KAM theory for reversible systems, the author proves the existence of invariant tori and thus the boundedness of all the solutions and the existence of quasiperiodic solutions and subharmonic solutions.

Let X={X_t,t≥0} be a d-dimensional (d≥2) standard Brownian motion with drift c started at a fixed x, and B_R={x∈ℝ^d:|x|<R}, the ball centered at 0 with radius R. Consider the distributions of T_R(t) and T_R(∞), where T_R(t) denotes the time spent by X in B_R up to time t and T_R(∞) the total time of X spent in B_R. Explicit formulas for the Laplace transform of T_R(∞) and the double Laplace transform of T_R(t) are obtained.

The authors prove the stability of the rings of highest weight vectors of the action of O_m×GL_n on the complex polynomial rings on . As an application, the structure of the rings for m=3 is determined.

An intrinsic Harnack estimate and some sup-estimates are established for nonnegative weak solutions of equations of non-Newtonian polytropic filtration u_t-div(|Du^m|^p-2Du^m)=0, m(p-1)<1, m>0, p>1.

Let R be a hyperbolic Riemann surface of conformal infinite type. Denote by A the Banach space of all integrable holomorphic quadratic differentials on R, and by B₀ and B the predual and dual of A, respectively. This paper gives a complete description of the convexity of these three spaces.

It is conjectured that the manifold with nonnegative Ricci curvature and weaked bounded geometry is of finite topological type, if

This paper is devoted to the existence and the uniqueness of the entropy solution for a general scalar conservation law associated with a forced bilateral obstacle condition in a bounded domain of ℝ^p, p≥1.

The method of penalization is used with a view to obtaining an existence result. However, the former only gives uniform L^∞-estimates and so leads in fact to look for an Entropy Measure-Valued Solution, according to the specific properties of bounded sequences in L^∞. The uniquess of this EMVS is proved. Classically, it first ensures the existence of a bounded and measurable function U entropy solution and then the strong convergence in L^q of approximate solutions of U.

The authors study the continuous properties of square integrable g-martingales via backward stochastic differential equations (shortly BSDEs) and get a general upcrossing inequality and an optional stopping theorem for g-martingales.