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1.
We study the regularity of the minimizer u
for the functional F
(u,f)=|u|2 + |u–f{2 over all maps uH
1(, S
2). We prove that for some suitable functions f every minimizer u
is smooth in if 0 and for the same functions f, u
has singularities when is large enough.
Résumé On étudie la régularité des minimiseurs u du problème de minimisation minueH 1(,S2)(|u|2 + |u–f{2. On montre que pour certaines fonctions f, u est régulière lorsque 0 et pour les mêmes f, si est assez grand, alors u possède des singularités.相似文献
2.
The dual approach to the problem –u=u+u|u|2*–2, uþe
0
1
(gW), permits a simple proof of a recent existence result [5] and allows extensions of this result to similar problems also with asymmetric mnonlinearities.Supported by min P.I., Gruppo Naz. (40%) Calcolo delle Variazioni... 相似文献
3.
本文中, 我们主要刻画了Toeplitz算子$T=M_{z^k}+M^*_{z^l}$的约化子空间, 其中 $k_i, l_i$ ($i=1,2$) 均是正整数, $k=(k_1,k_2), l=(l_1,l_2)$ 且 $k\neq l$, $M_{z^k}$, $M_{z^l}$ 是双圆盘加权Hardy空间$\mathcal{H}_\omega^2(\mathbb{D}^2)$上的乘法算子. 对权系数 $\omega$ 适当限制, 我们证明了由 $z^m$ 生成的 $T$ 的约化子空间均是极小的. 特别地, Bergman 空间和加权 Dirichlet 空间 $\mathcal{D}_\delta(\mathbb{D}^2)(\delta>0)$ 均是满足该限制条件的加权Hardy空间. 作为应用, 我们刻画了 $\mathcal{D}_\delta(\mathbb{D}^2)(\delta>0)$ 上 Toeplitz 算子 $T_{z^k+\bar{z}^l}$ 的约化子空间, 该结论是对双圆盘Bergman 空间上相关结论的推广. 相似文献
4.
5.
the Alternating Segment Crank-Nicolson scheme for one-dimensional diffusion equation has been developed in [1],and the Alternating Block Crank-Nicolson method for two-dimensional problem in [2].The methods have the advantages of parallel computing,stability and good accuracy.In this paper for the two-dimensional diffusion equation,the net region is divided into bands,a special kind of block.This method is called the alternating Band Crank-Nicolson method. 相似文献
6.
导出边值问题△^2u-s△u k^2u=0;x∈Ω∪Ω‘∪→R^2;u/Γ=u0;δu/δn/Γ=g0的定解问题,MRM边界变分方程,全平面解的表达式,从中可以以看出,MRM边界变分方程中只包含弱奇异积分核,并且自动消除了原第一,二MRM边界积分方程中出现的强奇异积分核,问题解的表达式后并不加任何多项式,因而也不需要引入Lagrange乘子求解该项,这给边界元数值求解过程带来极大的方便,数值分析结果表明该方法具有明显优势。 相似文献
7.
Gradient Estimates and Harnack Inequalities for Positive Solutions of $$\mathfrak{L}u=\frac{\partial u}{\partial t}$$ L u = ∂ u ∂ t on Self-shrinkers
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In this paper, we investigate the positive solutions of Lu=∂u/∂t on self-shrinkers, then get some gradient estimates and Harnack inequalities for the positive solutions. 相似文献
8.
设 $p\geq 7$ 为任意奇素数. 证明了当 $3\leq s
相似文献
9.
饶若峰 《数学年刊A辑(中文版)》2005,(6)
本文利用山路引理以及P.L.Lions的集中紧性原理,给出了具临界指数2*且涉及任意特征值λk 的Dirichlet问题-△u=λku |u|2*-2u f(x,u)一对非平凡解的存在性定理,其中次临界扰动项 f(x,t)可以是关于变量t的非线性项. 相似文献
10.
Koichi Betsumiya T. Aaron Gulliver Masaaki Harada 《Designs, Codes and Cryptography》2003,28(2):171-186
In this paper, it is shown that extremal (Hermitian) self-dual codes over
2 ×
2 exist only for lengths 1, 2, 3, 4, 5, 8 and 10. All extremal self-dual codes over
2 ×
2 are found. In particular, it is shown that there is a unique extremal self-dual code up to equivalence for lengths 8 and 10. Optimal self-dual codes are also investigated. A classification is given for binary [12, 7, 4] codes with dual distance 4, binary [13, 7, 4] codes with dual distance 4 and binary [13, 8, 4] codes with dual distance 4. 相似文献
11.
本文利用山路引理以及P.L.Lions的集中紧性原理,给出了具临界指数2*且涉及任意特征值λk的Dirichlet问题-△u=λku+|u|2*-2u+f(x,u)一对非平凡解的存在性定理,其中次临界扰动项f(x,t)可以是关于变量t的非线性项. 相似文献
12.
Jean-François Le Gall 《Probability Theory and Related Fields》1995,102(3):393-432
Summary We investigate the connections between the path-valued process called the Brownian snake and nonnegative solutions of the partial differential equation u=u
2 in a domain of
d
. In particular, we prove two conjectures recently formulated by Dynkin. The first one gives a complete characterization of the boundary polar sets, which correspond to boundary removable singularities for the equation u=u
2. The second one establishes a one-to-one correspondence between nonnegative solutions that are bounded above by a harmonic function, and finite measures on the boundary that do not charge polar sets. This correspondence can be made explicit by a probabilistic formula involving a special class of additive functionals of the Brownian snake. Our proofs combine probabilistic and analytic arguments. An important role is played by a new version of the special Markov property, which is of independent interest. 相似文献
13.
本文探讨模同态广义逆在环模理论中的应用.利用模同态的{1}-逆与{2}-逆,分别给出了一类环及一类重要模的特征刻画. 相似文献
14.
We investigate the structure of codes over
rings with respect to the Rosenbloom-Tsfasman (RT) metric. We define a standard form generator matrix and show how we can
determine the minimum distance of a code by taking advantage of its standard form. We define MDR (maximum distance rank) codes
with respect to this metric and give the weights of the codewords of an MDR code. We explore the structure of cyclic codes
over
and show that all cyclic codes over
rings are MDR. We propose a decoding algorithm for linear codes over these rings with respect to the RT metric.
AMS Classification: 94B05, 94B60 相似文献
15.
María Martí Sánchez 《Geometriae Dedicata》2011,150(1):49-61
This note describes minimal surfaces S of general type satisfying p
g
≥ 5 and K
2 = 2p
g
. For p
g
≥ 8 the canonical map of such surfaces is generically finite of degree 2 and the bulk of the paper is a complete characterization
of such surfaces with non birational canonical map. It turns out that if p
g
≥ 13, S has always an (unique) genus 2 fibration, whose non 2-connected fibres can be characterized, whilst for p
g
≤ 12 there are two other classes of such surfaces with non birational canonical map. 相似文献
16.
17.
本文探索了环$R=Z_4[u]/\langle u2-2\rangle$ 上的几类斜多元循环码和多元循环码. 首先得到了环$R$上$(1,2u)$-多元循环码的生成多项式. 其次由定义的Gray映射得到了环$R$上$(1,2u)$- 多元循环码的Gray像是$Z_4$上的循环码或指数为2的逆循环码. 最后, 通过环$R$上$(1,2u)$- 多元循环码的一些例子来展示本文的主要结果. 相似文献
18.
Jeremy Maitin-Shepard 《Designs, Codes and Cryptography》2017,82(1-2):301-318
Field inversion in \(\mathbb {F}_{2^{m}}\) dominates the cost of modern software implementations of certain elliptic curve cryptographic operations, such as point encoding/hashing into elliptic curves (Brown et al. in: Submission to NIST, 2008; Brown in: IACR Cryptology ePrint Archive 2008:12, 2008; Aranha et al. in: Cryptology ePrint Archive, Report 2014/486, 2014) Itoh–Tsujii inversion using a polynomial basis and precomputed table-based multi-squaring has been demonstrated to be highly effective for software implementations (Taverne et al. in: CHES 2011, 2011; Oliveira et al. in: J Cryptogr Eng 4(1):3–17, 2014; Aranha et al. in: Cryptology ePrint Archive, Report 2014/486, 2014), but the performance and memory use depend critically on the choice of addition chain and multi-squaring tables, which in prior work have been determined only by suboptimal ad-hoc methods and manual selection. We thoroughly investigated the performance/memory tradeoff for table-based linear transforms used for efficient multi-squaring. Based upon the results of that investigation, we devised a comprehensive cost model for Itoh–Tsujii inversion and a corresponding optimization procedure that is empirically fast and provably finds globally-optimal solutions. We tested this method on eight binary fields commonly used for elliptic curve cryptography; our method found lower-cost solutions than the ad-hoc methods used previously, and for the first time enables a principled exploration of the time/memory tradeoff of inversion implementations. 相似文献
19.
<正> 本文用逐步逼近法来解如下的柯西问题:这里q(x),f(x)是定义在全空间中的连续函数,并具有二阶有界导数。 相似文献
20.
本文利用Wahlquist-Estabrook过程(WEP)研究了方程(?)~2u/(?)x~1(?)x~1 (?)~2u/(?)x~2(?)x~2=f(u)(这里f是任意函数)的B(?)cklund变换.我们发现该方程存在B(?)cklund变换的充分条件是d~2f/du~2=λf.我们所得到的结果的一个特殊情况就是Leibbrandt的结论. 相似文献