C~(1,α)PARTIAL REGULARITY FOR SOLUTIONS OF NONLINEAR ELLIPTIC SYSTEMS

We use the blow-up method to get the C~(1,α) partial regularity results for the following elliptic systems satisfying natural growth conditions:     

THE REGULARITY OF SOLUTIONS FOR NONLINEAR DEGENERATE ELLIPTIC BOUNDARY VALUE PROBLEM

This paper is devoted lo the study of regularity of solutions for Dirichlet probelm ofnonlinear degenerate elliptic equations in two dimensional case. A sufficient condition fortheir solutions in C~(3+α)(Ω) to be certainly in C~∞(Ω) is given.     

C~(1,α)-PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS

Ｃ~（１，α）－ＰＡＲＴＩＡＬＲＥＧＵＬＡＲＩＴＹＦＯＲＮＯＮＬＩＮＥＡＲＥＬＬＩＰＴＩＣＳＹＳＴＥＭＳＴａｎｚｈｏｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉａｍｅｎＵｎｉｖｅｒｓｉｔｙ，Ｘｉａｎｍｅｎ３６１００５，Ｃｈｉｎａ．）Ａｂ?..     

L~∞ESTIMATE FOR SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS IN R~N

Ｌ~∞ＥＳＴＩＭＡＴＥＦＯＲＳＯＬＵＴＩＯＮＳＯＦＮＯＮＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳＩＮＲ~ＮＬｉＧｏｎｇｂａｏ（李工宝）（Ｉｎｓｔ．ｏｆＭａｔｈ．Ｓｃｉ．，ＴｈｅＣｈｉｎｅｓｅＡｃａｃｌｅｍｙｏｆＳｃｉｅｎｃｅｓＳｉｎｉｃａ，ＰＯＢ...     

H~1 SOLUTIONS FOR A CLASS OF SEMILINEAR PARABOLIC SYSTEMS

1IntroductionInthispapertweconsiderthefollowingsystemswithinitialvaluewhereu=(tLt,'',Wi),F=(FI,'.',Fn),t20,--co0,thereisasolutionu(x,f)of(1.1),suchthatIIullHI5C(T).C(T)isaconstantdependingboundlyon"o(z)andT.Ifb=0,then(1.l)isthetypicalselnilinearheatsystems,i.e.therearemugpapersdealingwiththesystems(1.3).Theinvestigationill…     

对角形椭圆组H~1∩L~(n(r-1)/(2-r))弱解的处处正规性

考虑对角性拟线性椭园组 -D_β(A~(αβ)(x,u)D_αu~i)=B_i(x,u,Du),x∈Ω,i=1,…,N。 (1)这里Ω是R~n中的有界域。重复上、下标α、β表示从1到n求和,D_u={D_αu~i|α=1,…     

REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI COEFFICIENTS UNDER NATURAL GROWTH CONDITION FOR THE CASE：1〈m〈2

In this article,we consider interior regularity for weak solutions to nonlinear elliptic systems of divergence type with Dini continuous coefficients under natural growth condition for the case 1相似文献   

OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS UNDER THE NATURAL GROWTH CONDITION： THE METHOD OF A-HARMONIC APPROXIMATION

In this article,the authors consider the nonlinear elliptic systems under the natural growth condition.They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions,based on a generalization of the technique of harmonic approximation.And directly establish the optimal Holder exponent for the derivative of a weak solution.     

A NOTE ON THE CONSTRUCTION OF SYMPLECTIC SCHEMES FOR SPLITABLE HAMILTONIAN H = H~((1)) H~((2)) H~((3))

For a hamiltonian systemwhere J = [ 2: ], It, is n x n identity matrix, H f R2n - R is a smooth function andl It, O I t It, is n x n identity matrix, H f R2n - R is a smooth function and7 is the gradiellt operator, the 8ymplectic difference schemes should…     

巧用1/(n(n k))=1/k((1/n)-(1/(n k)))解竞赛题

一、用来解方程例1(1999年河北省竞赛题)方程1/(x(x-1)) 1/(x(x 1)) … 1/((x 1997)(x 1998)) =(1999)/(2000)的根为()．(A)1999 (B)-2 (C)-1999或2 (D)1999或-2解根据公式原方程化为1/(x-1)-1/x 1/x-1/(x 1) … 1/(1/(x 1997))-1/(x 1998)=(1999)/(2000),1/(x-1)-1/(x 1998)=(1999)/(2000),(x 1998)-(x-1)=(1999)/(2000)(x-1)(x 1998),1999=(1999)/(2000)(x-1)(x 1998),     

ELLIPTIC H~2－VOLTERRA PROJECTION AND THE H~1－GALERKIN METHODS FOR THE INTEGRO－DIFFERENTIAL EQUATIONS OF EVOLUTION

ＥＬＬＩＰＴＩＣＨ~２－ＶＯＬＴＥＲＲＡＰＲＯＪＥＣＴＩＯＮＡＮＤＴＨＥＨ~１－ＧＡＬＥＲＫＩＮＭＥＴＨＯＤＳＦＯＲＴＨＥＩＮＴＥＧＲＯ－ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＯＦＥＶＯＬＵＴＩＯＮ￥ＳＵＮＰＥＮＧＴＡＯＡｂｓｔｒａｃｔ：Ｔｈｉｓｐ...     

ON INTERPOLATION BY S_2~1(△_(m,n)~((2)))

Let △_(m,n)~(2)be a subdivision of D:[a,b]×[c,d](Fig.1),_1arelengths of[a,b]and[c,d]respectively,and h_1=_1/m,h_2=_2/n.     

STABILITY OF SOLUTIONS FOR THE RECURSIVE SEQUENCE x_(n+1) =α-βx_n/γ+g(x_(n-1),…,x_(n-k))

In this paper, we study the stability of a class of recursive sequence under certain conditions.     

方程x_(n+1)=x_nexp[r_n((1-x_n)/(1-λx~n))]的全局吸引性

本文考虑非自治差分方程xn+ 1=xnexp[rn1- xn1-λxn]　 n=0 ,1,2 ,…的全局吸引性 ,这里 { rn}是正实数列 0 <λ<1我们获得了方程每一解趋于 1的充分条件 .     

EXACT SOLUTIONS OF (2+1)-DIMENSIONAL NONLINEAR SCHRöDINGER EQUATION BASED ON MODIFIED EXTENDED TANH METHOD

In this paper, the modified extended tanh method is used to construct more general exact solutions of a(2+1)-dimensional nonlinear Schr¨odinger equation.With the aid of Maple and Matlab software, we obtain exact explicit kink wave solutions, peakon wave solutions, periodic wave solutions and their 3D images.     

EXISTENCE AND UNIQUENESS OF LIMIT CYCLE FOR A CLASS OF (2n+1)TH ORDER DIFFERENTIAL SYSTEM

In this paper we consider the problem ofllrmt cycles for thefollowing system【&一y＋6x＋a旷＋a。xy＋a。xy‘＋6xv‘”,(门)!i二 X( 一 by)．Ssstem(1)with k二 b二 0 was studiedin P叩er[1];Ifk 4 0 by transformation:y三 x;V二告;d,二 kdt,system(1)。二。can be trmslated Into the form studiedIn p。per IZ]三 System(1)With口1二 k二 0 W。S Studied ill paper k3]．Ifi System(1;SllPPOSe th。t:(1 ＞2 Is。11 lllteger,k / 0*d 6 / oi(2)。1。2 ＋。5 2 0,this assumption Is the same as that In paper[1];(3)w…     

Drinfeld―Sokolov Reduction for Difference Lax Operators with Periodic Boundary Conditions in the Case of gl(n,C((λ-1)))

Within the framework of the method of formal dressing transformations, we construct a family of zero-curvature equations with discrete space variable for the case of the algebra gl(n,((^-1))). The equations obtained admit reduction with respect to the gauge group and, on the quotient, give rise to the $n$th order scalar difference equations that can be regarded as discrete analogs of KdV-equations. It is proved that the flows orresponding to different equations of the family commute. Bibliography: 10 titles.     

广义积分integral from n=0 to 1()((1n)~(k-1)t)/(1 t)dt与级数Sum from n=1 to ∞() ((-1)~(n-1))/n~k间的关系及计算

定理1设k是正整数，则有证明记由于易知又由于所以所以（6）式为在（8）中取、r—－1，有在（9）中作变换L—一X有＿＿、＿．l．＿＿、，＿I。〔h〔，＿＿＿rp（－1）＿。＿。L、，＿＿＿。。＿＿＿＿，＿。。定理1给出了广义积分l；：＝一体与级数西二个一之间的关系。下面的定理2将给出‘“““””“’””””“”JI＋t”’”””“‘“’””“““””“’””““”“”‘”“““计算级数Zirn／一的一个递推公式。它相9地将人X）展成余弦级数（14）式为一递推公式，继续递推并注意到八二I。。Snxdx一O，则（14）为在（16）式中…     

Bounds on the maximum numbers of clear two-factor interactions for 2~((n1+n2)-(k1+k2)) fractional factorial split-plot designs

Fractional factorial split-plot (FFSP) designs have an important value of investigation for their special structures. There are two types of factors in an FFSP design: the whole-plot (WP) factors and sub-plot (SP) factors, which can form three types of two-factor interactions: WP2fi, WS2fi and SP2fi. This paper considers FFSP designs with resolutionⅢorⅣunder the clear effects criterion. It derives the upper and lower bounds on the maximum numbers of clear WP2fis and WS2fis for FFSP designs, and gives some methods for constructing the desired FFSP designs. It further examines the performance of the construction methods.     

REGULARITY AND EXPLICIT REPRESENTATION OF (0,1,…,m - 2,m) INTERPOLATION ON THE ZEROS OF (1-x)P_(n-1)~(α,β)(x)

A necessary and sufficient condition of regularity of (0,1,…,m - 2,m) interpolation on the zeros of (1-x)P_(n-1)~(α,β)(x) (α> -1,β≥- 1) in a manageable form is established, where P_(n-1)~(α,β)(x) stands for the (n-1)th Jacobi polynomial. Meanwhile, the explicit representation of the fundamental polynomials when they exist, is given.