一类非齐次A-调和方程组很弱解的性质

该文应用Hodge分解定理，得到了非齐次A—调和方程组-Di(A^ij(x,Du)) Difj(i(x)=0,j=1,…，m的很弱解是弱解，进一步，利用Morrey空间法与Campanato空间法以及齐次化方法，作者得出了该方程的很弱解是局部Hoelder连续的，并且得出了Hoelder连续指数μ与λ之间的多值函数关系式．     

REGULARITY OF WEAK SOLUTION TO P-LAPLACIAN WITH MEASURABLE COEFFICIENT

Holder continuity and C1-regularity for the weak solution in W1,p to P-Laplacianwith measurable coefficient were obtained.     

一类拟线性椭圆方程的很弱解的唯一性

利用以极大函数表示的有关Sobolev函数的逐点不等式来构造全局的Lipschitz型检验函数,得到了,在一定条件下,拟线性椭圆方程-div A(x,u,Du)=f(x)在grand Sobolev空间W_0~(θ,p)(Ω)中的很弱解是唯一的．     

一类退缩的椭圆型方程弱解的正则性

本文给出了一类退缩的拟线性椭圆型方程－Ｄｉｖ「↓ｕ｜＾ｐ－２↓ｕ＋Ｆ（ｘ,ｕ）」＝Ｂ（ｘ,ｕ,↓ｕ）在Ｗ＾１,ｐ（Ω）中弱解的Ｃ＾１,λｌｏｃ（Ω）正则性,其中Ω为Ｒ＾Ｎ中行一区域。     

带有交叉扩散的捕食模型的非常数正稳态解的存在性

本文研究了下列带有交叉扩散的捕食模型的稳态问题的非常数正解的存在性,证明了当d4>1/m1v-u时存在(g1,d2,d3)使得稳态问题存在非常数正解;而当d4≤1/m1v-u或者d1≥m1v-u/u1或者a(m1b,a2(b))时稳态问题不存在非常数正解．     

一类非齐次A-调和方程组很弱解的正则性

本文应用Hodge分解定理,得到了非齐次A-调和方程组 -Di（Aij（x,u,Du））+Bj（x,u,Du）=0,j=1,…,m的很弱解的局部W1,q-正则性,从而推广了文献[6-8]有关的结果.     

一类拟线性椭圆方程的很弱解的唯一性

利用以极大函数表示的有关Sobolev函数的逐点不等式来构造全局的Lipschitz型检验函数,得到了在一定条件下,拟线性椭圆方程-divA(x, u, Du) = f(x)在grand sobolev空间W0θ,p)(Ω)中的很弱解是唯一的.     

ON A SEMILINEAR MRABOLIC EQUATION SYSTEM WITH NONLOCAL AND COUPLED BOUNDARY CONDITIONS

1IntroductionInthestudyofquasi-statethermoelasticity,Deng[1-2]derivedamathemati-calmodelwhichinvolvesalinearparabolicequationwithanonlocalboundarycondition.Thismodelhasbeenextendedtomoregeneralsemilinearparabo-licequationsinhigh-dimensiondomainsbyFriedman[5]andKawohlI6],andmorerecentlybyDeng[3],Yin[13],Paol8-lo]andWang[11],andvariouscomparison,estimateandstabilityresultshavebeenobtained.InhtispaperweextendtheproblemofPao[9]tothefollowingproblemwithmoregeneralcoupledboundaryconditions(PE):w…     

REGULARITY FOR CERTAIN QUASILINEAR ELLIPTIC SYSTEMS OF DIVERGENCE STRUCTURE

1 IntroductionEnter section title between curly braces In [1], partiaJ H6lder continuity of the gradient ofsolution to elliptic systems of the formunder the assumption that the solutions u E C',,(O). In general, we can only obtain the Co,o-regularity see [2]-[6]. Under strong assumption can we obtain Co,l- regularity t see f7J. In thepresent paper a partial COl"-regularity and E- regularity theorem are derived fOr the gradientof solutions of elliptic systems of the formin a domain fl in …     

一类A-调和方程的障碍问题的很弱解的全局正则性

应用Hodge分解定理,得到了非齐次A-调和方程-div(A(x,Du(x)))=f(x,u(x))对应的障碍问题很弱解的局部和全局的W~(1,q)(Ω)-正则性,其中,A(x,Du(x)),f(x,u(x))满足文中所给的条件,从而推广了相关文献中的有关结果.该结果在优化控制问题中有着广泛的应用.