共查询到20条相似文献,搜索用时 265 毫秒
1.
2.
3.
On Singular Sets of Local Solutions to p-Laplace Equations 总被引:1,自引:1,他引:0
Hongwei LOU 《数学年刊B辑(英文版)》2008,29(5)
The author proves that the right-hand term of a p-Laplace equation is zero on the singular set of a local solution to the equation. Such a result is used to study the existence of an optimal control problem. 相似文献
4.
The authors study a family of transcendental entire functions which
lie outside the Eremenko-Lyubich class in general and are of
infinity growth order. Most importantly, the authors show that the
intersection of Julia set and escaping set of these entire functions
has full Hausdorff dimension. As a by-product of the result, the
authors also obtain the Hausdorff measure of their escaping set is
infinity. 相似文献
5.
本文研究了平面上的亚纯函数的奇异方向,利用Tsuji’s的第二基本定理和几个已有的关于函数增长性估计的引理,证明了平面上的零级亚纯函数至少存在一条T方向,这种方向直接以特征函数为比较函数,克服了Borel方向的定义中关于增长级不能为零的限制. 相似文献
6.
Xinfu Chen Huiqiang Jiang 《Calculus of Variations and Partial Differential Equations》2012,44(1-2):221-246
In this paper, we consider a singular elliptic equation modeling steady states of a dewetting thin film model with both van der Waals and Born repulsion force. We show that as the Born repulsion force tends to zero, the energy minimizers, passing to a subsequence if necessary, converge to a Dirac mass located on the boundary. We also identify the blow up profile of the energy minimizers. 相似文献
7.
GEOMETRY AND DIMENSION OF SELF—SIMILAR SET 总被引:1,自引:0,他引:1
The authors show that the self-similar set for a finite family of contractive similitudes (similarities, i.e., |fi(x) - fi(y)| = αi|x - y|, x,y ∈ RN, where 0 < αi < 1) is uniformly perfect except the case that it is a singleton. As a corollary, it is proved that this self-similar set has positive Hausdorff dimension provided that it is not a singleton. And a lower bound of the upper box dimension of the uniformly perfect sets is given. Meanwhile the uniformly perfect set with Hausdorff measure zero in its Hausdorff dimension is given. 相似文献
8.
A capacity estimate for the blow-up set of parabolic equations is derived. It refines the Lebesgue measure estimate (Sakaguchi
and Suzuki in Arch Rational Mech Anal 142:143–153, 1998), includes the result on the elliptic case (T. Sato, T. Suzuki, F.
Takahashi, in p-capacity of the singular set of p-harmonic function vanishes, preprint), and provides information on the profile of any post-blow-up solution.
相似文献
9.
S. E. Kholodovskii 《Differential Equations》2013,49(12):1655-1660
We derive analytic formulas that, on the basis of given harmonic functions, permit one to construct solutions of boundary value problems on a plane containing an infinitely thin three-layer film by simple quadratures with the preservation of singular points of the harmonic functions. The three-layer film consists of alternating strongly and weakly permeable layers and has the form of a ray, a segment, or a circle arc. 相似文献
10.
11.
Hongwei LOU 《数学年刊B辑(英文版)》2008,29(5):521-530
The author proves that the on the singular set of a local solution to existence of an optimal control problem. right-hand term of a p-Laplace equation is zero the equation. Such a result is used to study the 相似文献
12.
一类非线性压缩生成的不变集的局部维数 总被引:1,自引:0,他引:1
本文以有界变差原理和有界畸变原理为工具,讨论了满足开集条件,且二次可微的一族递增的非线性压缩映射所产生的不变集的局部维数。 相似文献
13.
We consider the linear parabolic equation describing the transport of a contaminant in a porous media crossed by a net of infinitely thin fractures. The permeability is very high in the fractures but very low in the porous blocks. We derive the homogenized model corresponding to a net of infinitely thin fractures, by means of the singular measures technique. We assume that these singular measures are supported by hyperplanes of codimension one. We prove in a second step that this homogenized model could be obtained indistinctly either by letting the fracture thickness, in the standard double porosity model, tend to zero, or by homogenizing a model with infinitely thin fractures. 相似文献
14.
Finite difference methods are used to estimate the error in approximations to functions defined by differential equations. The problem of minimising the maximum of this error estimate can be solved by linear programming in the linear case, and by a method due to the authors in the nonlinear case. It is shown by examples that this new approach can improve substantially on techniques which minimise the maximum residual in the differential equation, and a convergence result as the mesh spacing tends to zero is given for the linear case. 相似文献
15.
Juan Fernández Sánchez Pelegrí Viader Jaume Paradís Manuel Díaz Carrillo 《Nonlinear Analysis: Theory, Methods & Applications》2012
This paper exhibits, for the first time in the literature, a continuous strictly increasing singular function with a derivative that takes non-zero finite values at some points. For all the known “classic” singular functions—Cantor’s, Hellinger’s, Minkowski’s, and the Riesz–Nágy one, including its generalizations and variants—the derivative, when it existed and was finite, had to be zero. As a result, there arose a strong suspicion (almost a conjecture) that this had to be the case for any singular function. We present here a singular function, constructed as a patchwork of known classic singular functions, with derivative 1 on a subset of the Cantor set. 相似文献
16.
17.
周脉东 《纯粹数学与应用数学》2012,(1):80-84
自仿测度的谱与非谱问题近年引起了很大的关注,关于自仿测度的非谱问题,其中之一就是要估算它在L2空间上的正交指数的个数.通过对μM,D傅里叶变换的零点集性质的分析和讨论,对现有的结论进行了改进,确定了相应四元素数字集的平面自仿测度在L2的空间上正交指数函数的最大个数为3. 相似文献
18.
V. M. Babich D. B. Dement'ev B. A. Samokish V. P. Smyshlyaev 《Journal of Mathematical Sciences》2004,122(5):3453-3458
An analytic expression for the electromagnetic wave scattered in singular directions on the vertex of a perfectly conducting cone is obtained. The approach used in the paper is a generalization to the electromagnetic case of the approach previously developed by the authors. In singular directions, the spherical front set of a wave scattered by the vertex is tangent to the front set of a wave reflected by the cone surface. The wave field is expressed in terms of parabolic-cylinder functions. Bibliography: 8 titles. 相似文献
19.
The authors establish the weak type endpoint estimate for the maximal commutators generated by Calderon-Zygmund singular integrals and Orlicz type functions with non-doubling measures. 相似文献
20.
用模糊集合与模糊等价关系对单向奇异粗集进行了研究,并给出了单向奇异粗糙模糊集合的数学结构及其并、交、补运算和性质.同时证明了单向奇异粗糙模糊集合对并、交、补运算构成完全可无限分配的软代数. 相似文献