The aim of this paper is to get the decomposition of distributional derivatives of functions with bounded variation in the framework of Carnot-Caratheodory spaces (C-C spaces in brievity) in which the vector fields ar...The aim of this paper is to get the decomposition of distributional derivatives of functions with bounded variation in the framework of Carnot-Caratheodory spaces (C-C spaces in brievity) in which the vector fields are of Carnot type. For this purpose the approximate continuity of BV functions is discussed first, then approximate differentials of L1 functions are defined in the case that vector fields are of Carnot type and finally the decomposition Xu = (?)u ·Ln + X2 u is proved, where u ∈ BVx(?) and (Ω)u denotes the approximate differential of u.展开更多
In this article, the authors consider equation ut = div（φ（Γu）A（｜Du｜^2）Du） - （u- I）, where φ is strictly positive and F is a known vector-valued mapping, A ： R＋ → R^＋ is decreasing and A（s） -1/ √s a...In this article, the authors consider equation ut = div（φ（Γu）A（｜Du｜^2）Du） - （u- I）, where φ is strictly positive and F is a known vector-valued mapping, A ： R＋ → R^＋ is decreasing and A（s） -1/ √s as s → ＋∞. This kind of equation arises naturally from image denoising. For an initial datum I ∈ BVloc ∩ L^∞, the existence of BV solutions to the initial value problem of the equation is obtained.展开更多
设f(x)在[0,∞)的每一有限子区间上为有界变差函数,作用在f(x)上的Szasz—Mirakyan算子和Baskakov算子分别为:S,(f,x)=sum from k=0 to ∞ (f(k/n)e^(nx)((nx)~k)/kl),V_n(f,x)=sum from k=0 to ∞ (f(k/n)((n+k-1)/k))x^k/(1+x)^(n+k))...设f(x)在[0,∞)的每一有限子区间上为有界变差函数,作用在f(x)上的Szasz—Mirakyan算子和Baskakov算子分别为:S,(f,x)=sum from k=0 to ∞ (f(k/n)e^(nx)((nx)~k)/kl),V_n(f,x)=sum from k=0 to ∞ (f(k/n)((n+k-1)/k))x^k/(1+x)^(n+k)) Fuhua Cheng借助Bojanic的方法得出了S_n(f,x)对f(x)的点态逼近度。本文在学习与参考[2]的基础上,更多地应用概率方法,来研究V_n(f,x)对f(x)的点态逼近度。在处理尾部时,我们得到了一个一般性的结果(文中的引理5),它不仅可以用来证明本文的定理1,而且也适用于其他算子,从而简化了[2]中的计算。展开更多
In this paper, we study the asymptotic behavior of minimizers (as ε→0) of the variational problems under Dirichlet conditioninf∫ Ω[ε p-1 |Du| p+1εW(x,u)]dx: u∈W 1,p (Ω), u=g, x∈ΩwhereW(x,·) is...In this paper, we study the asymptotic behavior of minimizers (as ε→0) of the variational problems under Dirichlet conditioninf∫ Ω[ε p-1 |Du| p+1εW(x,u)]dx: u∈W 1,p (Ω), u=g, x∈ΩwhereW(x,·) is a nonnegative function with only two zeros α and β. We show that the limit of a sequence of minimizers {u ε} ε>0 (as ε→0) is a solution of another variational problem.展开更多
The order of magnitude of multiple Fourier coefficients of complex valued functions of generalized bounded variations like （∧^1,.. .,∧^N）BV^（p） and r-BV, over [0,2π]^ N, are estimated.
文摘The aim of this paper is to get the decomposition of distributional derivatives of functions with bounded variation in the framework of Carnot-Caratheodory spaces (C-C spaces in brievity) in which the vector fields are of Carnot type. For this purpose the approximate continuity of BV functions is discussed first, then approximate differentials of L1 functions are defined in the case that vector fields are of Carnot type and finally the decomposition Xu = (?)u ·Ln + X2 u is proved, where u ∈ BVx(?) and (Ω)u denotes the approximate differential of u.
基金This research is partially supported by NSAF of China (10576013)by NSFC of China (10531040)
文摘In this article, the authors consider equation ut = div（φ（Γu）A（｜Du｜^2）Du） - （u- I）, where φ is strictly positive and F is a known vector-valued mapping, A ： R＋ → R^＋ is decreasing and A（s） -1/ √s as s → ＋∞. This kind of equation arises naturally from image denoising. For an initial datum I ∈ BVloc ∩ L^∞, the existence of BV solutions to the initial value problem of the equation is obtained.
文摘设f(x)在[0,∞)的每一有限子区间上为有界变差函数,作用在f(x)上的Szasz—Mirakyan算子和Baskakov算子分别为:S,(f,x)=sum from k=0 to ∞ (f(k/n)e^(nx)((nx)~k)/kl),V_n(f,x)=sum from k=0 to ∞ (f(k/n)((n+k-1)/k))x^k/(1+x)^(n+k)) Fuhua Cheng借助Bojanic的方法得出了S_n(f,x)对f(x)的点态逼近度。本文在学习与参考[2]的基础上,更多地应用概率方法,来研究V_n(f,x)对f(x)的点态逼近度。在处理尾部时,我们得到了一个一般性的结果(文中的引理5),它不仅可以用来证明本文的定理1,而且也适用于其他算子,从而简化了[2]中的计算。
文摘In this paper, we study the asymptotic behavior of minimizers (as ε→0) of the variational problems under Dirichlet conditioninf∫ Ω[ε p-1 |Du| p+1εW(x,u)]dx: u∈W 1,p (Ω), u=g, x∈ΩwhereW(x,·) is a nonnegative function with only two zeros α and β. We show that the limit of a sequence of minimizers {u ε} ε>0 (as ε→0) is a solution of another variational problem.
文摘The order of magnitude of multiple Fourier coefficients of complex valued functions of generalized bounded variations like （∧^1,.. .,∧^N）BV^（p） and r-BV, over [0,2π]^ N, are estimated.
