共查询到20条相似文献,搜索用时 9 毫秒
1.
Lingling Hou & Pengcheng Niu 《偏微分方程(英文版)》2020,33(4):341-376
In this paper we consider the divergence parabolic equation with bounded and measurable coefficients related to Hörmander's vector fields and establish a Nash type result, i.e., the local Hölder regularity for weak solutions. After deriving the parabolic Sobolev inequality, (1,1) type Poincaré inequality of Hörmander's vector fields and a De Giorgi type Lemma, the Hölder regularity of weak solutions to the equation is proved based on the estimates of oscillations of solutions and the isomorphism between parabolic Campanato space and parabolic Hölder space. As a consequence, we give the Harnack inequality of weak solutions by showing an extension property of positivity for functions in the De Giorgi class. 相似文献
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本文首先推广了Capogna,Danielli和Garofalo关于p-次Laplace算子的径向解的一个重要公式,然后通过改进欧氏空间中证明Laplace算子的Hopf引理的方法,证明了H型群上p-次Laplace算子的Hopf型引理,进而证明了一个强极大值原理。 相似文献
3.
In this paper, we are interested in the regularity estimates of the nonnegative viscosity super solution of the $β$−biased infinity Laplacian equation $$∆^β_∞u = 0,$$ where $β ∈ \mathbb{R}$ is a fixed constant and $∆^β_∞u := ∆^N_∞u + β|Du|,$ which arises from the random game named biased tug-of-war. By studying directly the $β$−biased infinity Laplacian equation, we construct the appropriate exponential cones as barrier functions to establish a key estimate. Based on this estimate, we obtain the Harnack inequality, Hopf boundary point lemma, Lipschitz estimate and the Liouville property etc. 相似文献
4.
Weiyang Chen & Xiaoli Chen 《数学研究》2014,47(2):208-220
In this paper, we are concerned with the properties of positive solutions of the following nonlinear integral systems on the Heisenberg group $\mathbb{H}^n$, \begin{equation} \left\{\begin{array}{ll} u(x)=\int_{\mathbb{H}^n}\frac{v^{q}(y)w^{r}(y)}{|x^{-1}y|^\alpha|y|^\beta}\,dy,\\ v(x)=\int_{\mathbb{H}^n}\frac{u^{p}(y)w^{r}(y)}{|x^{-1}y|^\alpha|y|^\beta}\,dy,\\ w(x)=\int_{\mathbb{H}^n}\frac{u^{p}(y)v^{q}(y)}{|x^{-1}y|^\alpha|y|^\beta}\,dy,\\ \end{array}\right.\end{equation} for $x\in \mathbb{H}^n$, where $0<\alpha
1$ satisfying $\frac{1}{p+1} $+ $\frac{1}{q+1} + \frac{1}{r+1} = \frac{Q+α+β}{Q}.$ We show that positive solution triples $(u,v,w)\in L^{p+1}(\mathbb{H}^n)\times L^{q+1}(\mathbb{H}^n)\times L^{r+1}(\mathbb{H}^n)$ are bounded and they converge to zero when $|x|→∞.$ 相似文献
5.
证明了一类海森堡群上半空间内与次拉普拉斯算子相关的最佳Hardy不等式.作为应用,我们得到了相应的最佳Rellich型不等式. 相似文献
6.
Matthieu Felsinger 《偏微分方程通讯》2013,38(9):1539-1573
Weak solutions to parabolic integro-differential operators of order α ∈ (α0, 2) are studied. Local a priori estimates of Hölder norms and a weak Harnack inequality are proved. These results are robust with respect to α↗2. In this sense, the presentation is an extension of Moser's result from [20]. 相似文献
7.
讨论了具间断系数的N维拟线性椭圆方程. 利用估计和差分逼近方法,证明了弱解的一阶导数H\"{o}lder连续到方程系数间断的内边界. 相似文献
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Local W^{1,q} estimates for weak solutions to a class of equations in divergence form D_i(a_{ij}(x)|Du|^{p-2D_ju) = 0 are obtained, where q > p is given. These estimates are very important in obtaining higher regularity for the weak solutions to elliptic equations. 相似文献
10.
本文用上下解方法,获得半线性次椭圆方程Dirichlet问题的-些存在性结果. 相似文献
11.
Existence Results for the Positive Solutions of a Fourth Order Nonlinear Equations on the Heisenberg Group 下载免费PDF全文
In this paper, we give some existence results for a fourth order nonlinear subelliptic equations on the Heisenberg group by the Leray-Schauder degree. 相似文献
12.
给出四元素Heisenberg群上次Laplace算子的平均值定理,并用其导出Hardy不等式和不确定原理. 相似文献
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In this paper, the Almgren’s frequency function of the following sub-elliptic equation with singular potential on the Heisenberg group: $$- \mathcal{L}u + V\left( {z,t} \right)u = - X_i \left( {a_{ij} \left( {z,t} \right)X_j u} \right) + V\left( {z,t} \right)u = 0$$ is introduced. The monotonicity property of the frequency is established and a doubling condition is obtained. Consequently, a quantitative proof of the strong unique continuation property for such equation is given. 相似文献
16.
In this paper, sufficient and necessary conditions for the first order interpolation inequalities with weights on the Heisenberg
group are given. The necessity is discussed by polar coordinates changes of the Heisenberg group. Establishing a class of
Hardy type inequalities via a new representation formula for functions and Hardy-Sobolev type inequalities by interpolation,
we derive the sufficiency. Finally, sharp constants for Hardy type inequalities are determined. 相似文献
17.
Littlewood Paley g-function on the Heisenberg Group 总被引:2,自引:0,他引:2
He Ping LIU Rui Qin MA 《数学学报(英文版)》2006,22(1):95-100
We consider the g-function related to a class of radial functions which gives a characterization of the L^p-norm of a function on the Heisenberg group. 相似文献
18.
Heisenberg群上非线性方程的特征值问题 总被引:1,自引:0,他引:1
本文研究Heisenberg群上非线性特征值问题,利用Lerny-Schauder度给出一些存在性结果及解集的性质. 相似文献
19.
Jingxuan Fang & Jiman Zhao 《分析论及其应用》2016,32(3):242-271
We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition and molecular decomposition we get the boundedness of singular integral operators on variable Hardy spaces. We investigate the Littlewood-Paley characterization by virtue of the boundedness of singular integral operators. 相似文献
20.
设 F是λ阶正则的齐次分布,-Q≤λ<0。作者研究了Heisenberg群上的算子g*F在加幂权的Lebesgue空间和Herz型 Hardy空间上的有界性,其中 g是一恰当的函数。而且,本文还得到了由BMO(H~n)函数和线性算子T所生成的交换子[b,T]在Herz空间上的有界性。 相似文献