In this paper,the global BMO estimates for the gradient of weak solutions to a class of elliptic equation obstacle problems is considered by using the Hardy-Littlewood maximal functions,the Jensen inequality for Young function,the perturbation method and other techniques.

本文研究一类具有可变指数的散度型椭圆方程Dirichlet问题弱解的全局H?lder连续性.通过建立反向H?lder不等式,并利用比较估计的方法,获得了所考虑问题弱解的全局C1,α连续性,推广了已有结论.

本文研究自然增长条件下一类具有H?lder连续系数的椭圆方程弱解梯度的全局BMO估计.在系数矩阵A为H?lder连续并满足一致椭圆条件下,利用极大函数方法,获得非线性Calderón-Zygmund型全局BMO估计.

本文研究一类非线性椭圆方程的Krψ,θ(?)-障碍问题很弱解u的全局可积性,其中u的可积指数r满足max{1,p?1}r,则上述问题的很弱解u具有全局可积性,这里r充分接近p.

研究一类A-调和方程对应障碍问题弱解的局部梯度估计,首先获得其局部Lp估计,然后再使用新标准化方法和迭代覆盖逼近方法将其推广到Orlicz空间.

该文主要研究一类自然增长条件下的非齐次A-调和方程弱解的梯度估计,首先获得自然增长条件下的非齐次A-调和方程弱解的Lp估计,然后使用迭代覆盖逼近方法等,将其推广到Orlicz空间.

该文主要研究Orlicz空间中A-调和方程很弱解的梯度估计,其中算子A满足某些合适的条件,给定的向量函数满足适当的增长条件.

在Rn(n≥2)中的有界区域Ω的边界?Ω满足可测密度条件下,研究了非齐次A-调和方程-divΑ(x,▽u)=-divF(x)对应的障碍问题的弱解.通过建立全局逆H?lder不等式,借助H?lder不等式、Young不等式及Gehring引理等工具,得出该方程障碍问题弱解的全局正则性.

This article concerns the higher integrability of a very weak solution u is an element of theta + W-0(1,r) (Omega) for max{1, p - 1} < r < p < n to the Dirichlet problem of the nonlinear elliptic system -D(alpha)A(i)(alpha)(x, Du) = B-i(x, Du) in Omega, u = theta on partial derivative Omega, where A(x, Du) = (A(i)(alpha)(x, Du)) for alpha = 1, ... , n and i = 1, ... , m, and each entry of B(x, Du) = (B-i(x, Du)) for i = 1, ... , m satisfies the monotonicity and controllable growth. If theta is an element of W-1(,q)(Omega) for q > r, then we derive that the very weak solution u of above-mentioned problem is integrable with u is an element of {theta + L-weak(q*) (Omega) for 1 <= q < n, theta + L-tau(Omega) for q = n and 1 < tau < infinity, theta + L-infinity(Omega) for q > n, provided that r is sufficiently close to p, where q* = qn/(n - q).

The paper deals with very weak solutions u to boundary value problems of the nonhomogeneous p-harmonic equation. We show that, any very weak solution u to the boundary value problem is integrable provided that r is sufficiently close to p.

This paper studies the A-harmonic equation d*A(x,du) =0,and acquires the removable singularities for weakly A-harmonic tensors by means of the Hodge decomposition and Caccioppoli estimation.

In this paper, we provide an alternative approach to partially Hölder continuity of some quasilinear elliptic systems with discontinuous coefficients under natural growth. Here, we do it by way of the modified A-harmonic approximation and Caccippoli’s inequality.

The Imbedding Inequalities and Poincare Inequalities of Weakly A-harmonic tensors have been proved.

考虑微分形式的A-调和方程d*A(x,du) =0的弱解(即A-调和张量),通过建立A-调和张量的Caccioppoli估计,获得了A-调和张量的奇点可去性.

影响区域乃至整个世界经济发展的重要因素之一就是科技资源.科技资源的配置整合在京津冀一体化发展中发挥着重要的作用.本文分析京津冀科技资源配置的优势与劣势,提出促进京津冀一体化科技资源配置整合的措施.

考虑变指数A-调和方程divA(x,▽u)=B(x,▽u),给出其弱解的梯度的局部H(o)lder连续性.

In this paper, we study the existence of multiple solutions for the following quasilinear elliptic system:p*(t)|u-2β- △pu1-μ|-2u up1= α1u + β1-2|xp||xt|vβ2||u|u, x∈,|q*β- △qv-μ2 |v|q-2v αv(s)-2|2x|q=|x|sv + β2|uβ1||v2 |-2v, x∈,u(x) = v(x) = 0, x∈ .Multiplicity of solutions for the quasilinear problem is obtained via variational method.

The higher integrability for very weak solutions ofA-harmonic form equationsd*A(x,u,du)=B(x,u,du)has been proved.

The Caccioppoli inequality of weakly A -harmonic tensors has been proved, which can be used to consider the weak reverse Hölder inequality, regularity property, and zeros of weakly A -harmonic tensors.

We study the existence of multiple solutions for the following elliptic problem: -Δpu-μ|u|p-2u/|x|p=|u|p*(t)-2/|x|tu+λ|u|q-2/|x|su,u∈W01,p(Ω). We prove that if 1≤q