Semicontinuity of multiple integrals onW k,p (Ω, ℜ m )(k≥1)

This paper shows thatW ^1,p -quasiconvexity is a necessary and sufficient condition of swlsc (sw*lsc) for multiple integrals with a Caratheodory function as the variational function, bounded by

Unsmoothing over balls via plane wave decomposition

Let

Semigroup-valued solutions of the Gołąb-Schinzel type functional equation

Let (S, o) be a semigroup. We determine all solutions of the functional equation

Boundedness of solutions for sublinear reversible systems

We are concerned with the boundedness of all the solutions for second order differential equation

An end point estimate for maximal commutators

In this paper we prove that the maximal commutator of singular integral operator [b, T]^* satisfies the inequality:

On theT(1) theorem on product domains

The direct proof by R. R. Coifman and Y. Meyer of theT(1) Theorem of G. David and J. L. Journé is based on the following result. LetT be an operator associated to a kernelk(x, y) satisfying

On maximal operators along surfaces

In this paper, we establish the boundedness of the following maximal operator

On a multiplicative function on the set of shifted primes

It is proved that if ƒ(n) is a multiplicative function taking a valueζ on the set of primes such thatζ ³ = 1,ζ ≠ 1 andƒ ³(p ^r)=1 forr≥2, then there exists aθ ∈ (0, 1), for which

On the riemann zeta-function and the divisor problem II

Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of . If E ^*(t)=E(t)-2πΔ^*(t/2π) with , then we obtain

Uniform boundedness theorems for nearly additive mappings

We deal with mappings from a (not necessarily commutative) groupG into a Banach spaceY which are nearly additive in the sense of satisfying that for some constantK ≥ 0,

Extremal functions for the trudinger-moser inequality in 2 dimensions

We prove that theTrudinger-Moser constant

Integral estimates of the solutions to the helmholtz equation in unbounded domains

The following boundary value problem is studied:

The unitary connections on the complex Grassmann manifold

In the complex Grassmann manifold ℱ(m,n), the space of complexn-planes passes through the origin of C^m+n; the local coordinate of the space can be arranged into anm ×n matrixZ. It is proved that

Systems with nonextendable convergence of quasipolynomials

The system , where Λ={λ _n } is the set of zeros (of multiplicitiesm _n ) of the Fourier transform

Markov-Bernstein-type inequalities for classes of polynomials with restricted zeros

We prove that an absolute constantc>0 exists such that

Estimate of fourier transforms with respect to the system of generalized eigenfunctions of the Schrödinger operator with Stummel-type potential

Suppose thatА is a nonnegative self-adjoint extension to { } of the formal differential operator−Δu+q(x)u with potentialq(x) satisfying the condition {

一类二阶渐近周期微分方程的正同宿轨道

§ 1　IntroductionIn this note we are concerned with the asymptotically periodic second order equation-u″+α( x) u =β( x) uq +γ( x) up,　 x∈ R,( 1 )where1 相似文献   

BOUNDARY VALUE PROBLEM FOR A GENERALIZED LIENARD EQUATION

By coincidence degree, the existence of solution to the boundary value problem of a generalized Liénard equation

A note on regularity for a class of quasilinear elliptic equations

The following regularity of weak solutions of a class of elliptic equations of the form are investigated.